## Fun with numbers till 9999 !!!

Mathematical Genius- whoever did this, the first few are easy, he’s done it upto 9999
Mind Blowing…………………
1 is the multiplicative identity.
2 is the only even prime.
3 is the ! ! number of spatial dimensions we live in.
4 is the smallest number of colors sufficient to color all planar maps.
5 is the number of Platonic solids.
6 is the smallest perfect number.
7 is the smallest number of integer-sided rectangles that tile a rectangle so that no 2 rectangles share a common length.
8 is the largest cube in the Fibonacci sequence.
9 is the maximum number of cubes that are needed to sum to any positive integer.
10 is the base of our number system.
11 is the largest known multiplicative persistence.
12 is the smallest abundant number.
13 is the number of Archimedian solids.
14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.
15 is the smallest composite number n with the property that there is only one group of order n.
16 is the only number of the form xy=yx with x and y different integers.
17 is the number of wallpaper groups.
18 is the only number that is twice the sum of its digits.
19 is the maximum number of 4th powers needed to sum to any number.
20 is the number of rooted trees with 6 vertices.
21 is the smallest number of distinct squares needed to tile a square.
22 is the number of partitions of 8.
23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.
24 is the largest number divisible by all numbers less than its square root.
25 is the smallest square that can be written as a sum of 2 squares.
26 is the only number to be directly between a square and a cube.
27 is the largest number that is the sum of the digits of its cube.
28 is the 2nd perfect number.
29 is the 7th Lucas number.
30 is the largest number with the property that all smaller numbers relatively prime to it are prime.
31 is a Mersenne prime.
32 is the smallest 5th power (besides 1).
33 is the largest number that is not a sum of distinct triangular numbers.
34 is the smallest number with the property that it and its neighbors have the same number of divisors.
35 is the number of hexominoes.
36 is the smallest number (besides 1) which is both square and triangular.
37 is the maximum number of 5th powers needed to sum to any number.
38 is the last Roman numeral when written lexicographically.
39 is the smallest number which has 3 different partitions into 3 parts with the same product.
40 is the only number whose letters are in alphabetical order.
41 is the smallest number that is not of the form |2x – 3y|.
42 is the 5th Catalan number.
43 is the number of sided 7-iamonds.
44 is the number of derangements of 5 items.
45 is a Kaprekar number.
46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.
47 is the largest number of cubes that cannot tile a cube.
48 is the smallest number with 10 divisors.
49 is the smallest number with the property that it and its neighbors are squareful.
50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.
51 is the 6th Motzkin number.
52 is the 5th Bell number.
53 is the only two digit number that is reversed in hexadecimal.
54 is the smallest number that can be written as the sum of 3 squares in 3 ways.
55 is the largest triangula! ! r number in the Fibonacci sequence.
56 is the number of reduced 5 x 5 Latin squares.
57 = 111 in base 7.
58 is the number of commutative semigroups of order 4.
59 is the smallest number whose 4th power is of the form a4+b4-c4.
60 is the smallest number divisible by 1 through 6.
61 is the 6th Euler number.
62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways.
63 is the number of partially ordered sets of 5 elements.
64 is the smallest number with 7 divisors.
65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.
66 is the number of 8-iamonds.
67 is the smallest number which is palindromic in bases 5 and 6.
68 is the last 2-digit string to appear in the decimal expansion of .
69 has the property that n2 and n3 together contain each digit once.
70 is the smallest abundant number that is not the sum of some subset of its divisors.
71 divides the sum of the primes less than it.
72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.
73 is the smallest number (besides 1) which is one less than twice its reverse.
74 is the number of different non-Hamiltonian polyhedra with minimum number of vertices.
75 is the number of orderings of 4 objects with ties allowed.
76 is an automorphic number.
77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.
79 is a permutable prime.
80 is the smallest number n where n and n+1 are both products of 4 or more primes.
81 is the square of the sum of its digits.
82 is the number of 6-hexes.
83 is the number of zero-less pandigital squares.
84 is the largest order of a permutation of 14 elements.
85 is the largest n for which 12+22+32+…+n2 = 1+2+3+…+m has a solution.
86 = 222 in base 6.
87 is the sum of the squares of the first 4 primes.
88 is the only number known whose square has no isolated digits.
89 = 81 + 92
90 is the number of degrees in a right angle.
91 is the smallest pseudoprime in base 3.
92 is the number of different arrangements of 8 non-attacking queens on an 8×8 chessboard.
93 = 333 in base 5.
94 is a Smith number.
95 is the number of planar partitions of 10.
96 is the smallest number that can be written as the difference of 2 squares in 4 ways.
97 is the smallest number with the property that its first 3 multiples contain the digit 9.
98 is the smallest number with the property that its first 5 multiples contain the digit 9.
99 is a Kaprekar number.
100 is the smallest square which is also the sum of 4 consecutive cubes.
101 is the number of partitions of 13.
102 is the smallest number with three different digits.
103 has the property that placing the last digit first gives 1 more than triple it.
104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex.
105 is the largest number n known with the property that n – 2k ! ! is prime for k>1.
106 is the number of trees with 10 vertices.
107 is the exponent of a Mersenne prime.
108 is 3 hyperfactorial.
109 is the smallest number w! ! hich is palindromic in bases 5 and 9.
110 is the smallest number that is the product of two different substrings.
111 is the smallest possible magic constant of a 3 x 3 magic square of distinct primes.
112 is the side of the smallest square that can be tiled with distinct integer-sided squares.
113 is a permutable prime.
114 = 222 in base 7.
115 is the number of rooted trees with 8 vertices.
116 is a value of n for which n!+1 is prime.
117 is the smallest possible value of the longest edge in a Heronian Tetrahedron.
118 is the smallest number that has 4 different partitions into 3 parts with the same product.
119 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 8.
120 is the smallest number to appear 6 times in Pascal’s triangle.
121 is the only square known of the form 1+p+p2+p3+p4, where p is prime.
122 is the smallest number n>1 so that n concatenated with n-1 0’s concatenated with the reverse of n is prime.
123 is the 10th Lucas number.
124 is the smallest number with the property that its first 3 multiples contain the digit 2.
125 is the only number known that contains all its proper divisors as proper substrings.
126 = 9C4.
127 is a Mersenne prime.
128 is the largest number which is not the sum of distinct squares.
129 is the smallest number that can be written as the sum of 3 squares in 4 ways.
130 is the number of functions from 6 unlabeled points to themselves.
131 is a permutable prime.
132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.
133 is the smallest number n for which the sum of the proper divisors of n divides phi(n).
134 = 8C1 + 8C3 + 8C4.
! ! 135 = 11 + 32 + 53.
136 is the sum of the cubes of the digits of the sum of the cubes of its digits.
137 is the smallest prime with 3 distinct digits that remains prime if one of its digits is removed.
138 is the smallest possible product of 3 primes, one of which is the concatenation of the other two.
139 is the number of unlabeled topologies with 5 elements.
140 is the smallest harmonic divisor number.
141 is a Cullen number.
142 is the number of planar graphs with 6 vertices.
143 is the smallest quasi-Carmichael number in base 8.
144 is the largest square in the Fibonacci sequence.
145 = 1! + 4! + 5!
146 = 222 in base 8.
147 is the number of sided 6-hexes.
148 is the number of perfect graphs with 6 vertices.
149 is the concatenation of the first 3 positive squares.
150 is the smallest n for which n + n times the nth prime is square.
151 is a palindromic prime.
152 has a square comprised of the digits 0-4.
153 = 13 + 53 + 33.
154 is the smallest number which is palindromic in bases 6, 8, and 9.
155 is the sum of the primes between its smallest and largest prime factor.
156 is the number of graphs with 6 vertices.
157 is the largest number kn! ! own whose square contains the same digits as its successor.
158 is the number of planar partitions of 11.
159 is the number of isomers of C11H24.
160 is the number of 9-iamonds.
161 is a hexagonal pyramidal number.
162 is the smallest number that can be written as the sum of of 4 positive squares in 9 ways.
163 is the largest Heegner Number.
164 is the smallest number which is the concatenation of squares in two different ways.
165 = 11C3.
166 is the number of monotone Boolean functions of 4 variables.
167 is the smallest number whose 4th power begins with 4 identical digits
168 is the size of the smallest non-cyclic simple group which is not an alternating group.
169 is a square whose digits are non-decreasing.
170 is the smallest number n for which phi(n) and sigma(n) are both square.
171 has the same number of digits in Roman numerals as its cube.
172 = 444 in base 6.
173 has a square containing only 2 digits.
174 is the smallest number that can be written as the sum of of 4 positive distinct squares in 6 ways.
175 = 11 + 72 + 53.
176 is an octagonal pentagonal number.
177 is the number of graphs with 7 edges.
178 has a cube with the same digits as another cube.
179 has a square comprised of the digits 0-4.
180 is the total number of degrees in a triangle.
181 is a strobogrammatic prime.
182 is the number of connected bipartite graphs with 8 vertices.
183 is the smallest number n so that n concatenated with n+1 is square.
184 is a Kaprekar constant in base 3.
185 is the number of conjugacy classes in the automorphism group of the 8 dimensional hypercube.
186 is the number of degree 11 irreducible polynomials over GF(2).
187 is the smallest quasi-Carmichael number in base 7.
188 is the number of semigroups of order 4.
189 is a Kaprekar constant in base 2.
190 is th! ! e largest number with the property that it and its ditinct prime factors are palindromic in Roman numerals.
191 is a palindromic prime.
192 is the smallest number with 14 divisors.
193 is the only known odd prime n for which 2 is! ! not a primitive root of 4n2+1.
194 is the smallest number that can be written as the sum of 3 squares in 5 ways.
195 is the smallest value of n such that 2nCn is divisible by n2.
196 is the smallest number that is not known to reach a palindrome when repeatedly added to its reverse.
197 is a Keith number.
198 = 11 + 99 + 88.
199 is the 11th Lucas number.
200 is the smallest number which can not be made prime by changing one of its digits.
201 is a Kaprekar constant in base 4.
202 has a cube that contains only even digits.
203 is the 6th Bell number.
204 is the square root of a triangular number.
205 is the largest number which can not be writen as the sum of distinct primes of the form 6n+1.
206 is the smallest number that can be written as the sum of of 3 positive distinct squares in 5 ways.
207 has a 4th power where the first half of the digits are a permutation of the last half of the digits.
208 is the 10th tetranacci number.
209 is the smallest quasi-Carmichael number in base 9.
210 is the product of the first 4 primes.
211 has a cube containing only 3 different digits.
212 has a square with 4/5 of the digits are the same.
213 is a number whose product of digits is equal to its sum of digits.
214 is a value of n for which n!! – 1 is prime.
215 = 555 in base 6.
216 is th! ! e smallest cube that can be written as the sum of 3 cubes.
217 is a Kaprekar constant in base 2.
218 is the number of digraphs with 4 vertices.
219 is the number of space groups, not including handedness.
220 is the smallest amicable number.
221 is the number of Hamiltonian planar graphs with 7 vertices.
222 is the number of lattices on 10 unlabeled nodes.
223 is the smallest prime which will nor remain prime if one of its digits is changed.
224 is not the sum of 4 non-zero squares.
225 is an octagonal square number.
226 ???
227 is the number of connected planar graphs with 8 edges.
228 = 444 in base 7.
229 is the smallest prime that remains prime when added to its reverse.
230 is the number of space groups, including handedness.
231 is the number of partitions of 16.
232 is the number of 7×7 symmetric permutation matrices.
233 is the smallest number with the property that it and its neighbors can be written as a sum of 2 squares.
234 ???
235 is the number of trees with 11 vertices.
236 is the number of Hamiltonian circuits of a 4×8 rectangle.
237 is the smallest number with the property that its first 3 multiples contain the digit 7.
238 is the number of connected partial orders on 6 unlabeled elements.
239 is the largest number that cannot be written as a sum of 8 or fewer cubes.
240 is the smallest number with 20 divisors.
241 ???
242 is the smallest number n where n through n+3 all have the same number of divisors.
243 = 35.
244 is the smallest number (besides 2) that can be written as the sum of 2 squares or the sum of 2 5th powers.
245 is a stella octangula number.
246 = 9C2 + 9C4 + 9C6.
247 is the smallest possible difference between two integers that together contain each digit exactly once.
248 is the smallest number n>1 for which the arithmetic, geometric, and harmonic means of phi(n) and sigma(n) are all integers.
249 ???
250 ???
251 is the smallest number that can be written as the sum of 3 cubes in 2 ways.
252 is the 5th central binomial coefficient.
253 is the smalles! ! t non-trivial triangular star number.
254 is the smallest composite number all of whose divisors (except 1) contain the digit 2.
255 = 11111111 in base 2.
256 is the smallest 8th power (besides 1).
257 is a Fermat prime.
258 ???
259 = 1111 in base 6.
260 is the number of ways that 6 non-attacking bishops can be placed on a 4×4 chessboard.
261 is the number of essentially different ways to dissect a 16-gon into 7 quadrilaterals.
262 is the 9th meandric number.
263 is the largest known prime whose square is strobogrammatic.
264 is the largest known number whose square is undulating.
265 is the number of derangements of 6 items.
266 is the Stirling number of the second kind S(8,6).
267 is the number of planar partitions of 12.
268 is the smallest number whose product of digits is 6 times the sum of its digits.
269 ???
270 is a harmonic divisor number.
271 is the smallest prime p so that p-1 and p+1 are divisible by cubes.
272 is the 7th Euler number.
273 = 333 in base 9.
274 is the Stirling number of the first kind s(6,2).
275 is the number of partitions of 28 in which no part occurs only once.
276 is the sum of the first 3 5th powers.
277 ???
278 ???
279 is the maximum number of 8th powers needed to sum to any number.
280 is the number of ways 18 people around a round table can shake hands in a non-crossing way, up to rotation.
281 is the sum of the first 14 primes.
282 is the sum of its proper divisors that contain the digit 4.
283 = 25 + 8 + 35.
284 is an amicable number.
285 is the number of binary rooted trees with 13 vertices.
286 is the number of rooted trees with 9 vertices.
287 is the sum of consecutive primes in 3 different ways.
288 is the smallest non-palindrome non-square that when multiplied by its reverse is a square.
289 is a Friedman number.
290 has a base 3 representation that ends with its base 6 representation.
291 is the number of functional graphs on 8 vertices.
292 is the number of ways to make change for a dollar.
293 ???
294 is the number of planar 2-connected graphs with 7 vertices.
295 ???
296 is the number of partitions of 30 into distinct parts.
297 is a Kaprekar number.
298 ???
299 ???
300 is the largest possible score in bowling.
301 is a 6-hyperperfect number.
302 is the number of acyclic digraphs with 5 vertices.
303 has a cube that is a concatenation of other cubes.
304 ???
305 ???
306 ???
307 is a non-palindrome with a palindromic square.
308 is a heptagonal pyramidal number.
309 is smallest value of n for which sigma(n-1) + sigma(n+1) = sigma(2n).
310 = 1234 in base 6.
311 is a permutable prime.
312 = 2222 in base 5.
313 is a palindromic prime.
314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways.
315 = (4+3)(4+1)(4+5).
316 ???
317 is a value of n for which one less than the product of the first n primes is prime.
318 is the number of unlabeled partially ordered sets of 6 elements.
319 is the smallest number with the property that the partition with the largest product does not have a maximum number of parts.
320 is the maximum determinant of a 10 x 10 matrix of 0’s and 1’s.
321 is a number whose product of digits is equal to its sum of digits.
322 is the 12th Lucas number.
323 is the product of twin primes.
324 is the largest possible product of positive integers with sum 16.
325 is a 3-hyperperfect number.
326 ???
327 and its double and triple together contain every digit from 1-9 exactly once.
328 concatenated with its successor is square.
329 ???
330 = 11C4.
331 ???
332 ???
333 is the number of 7-hexes.
334 ???
335 is the number of degree 12 irreducible polynomials over GF(2).
336 = 8P3.
337 is a permutable prime.
338 ???
339 ???
340 is a value of n for which n!+1 is prime.
341 is the smallest pseudoprime in base 2.
342 = 666 in base 7.
343 is a strong Friedman number.
344 is an octahedral number.
345 is half again as large as the sum of its proper divisors.
346! ! ???
347 is a Friedman number.
348 is the smallest number whose 5th power contains exactly the same digits as another 5th power.
349 ???
350 is the Stirling number of the second kind S(7,4).
351 is the smallest number n where n, n+1, and n+2 are all products of 4 or more primes.
352 is the number of different arrangements of 9 non-attacking queens on an 9×9 chessboard.
353 is the smallest number whose 4th power can be written as the sum of 4 4th powers.
354 is the sum of the first 4 4th powers.
355 is the number of labeled topologies with 4 elements.
356 ???
357 has a base 3 representation that ends with its base 7 representation.
358 has a base 3 representation that ends with its base 7 representation.
359 has a base 3 representation that ends with its base 7 representation.
360 is the number of degrees in a circle.
361 ???
362 and its double and triple all use the same number of digits in Roman numerals.
363 ???
364 = 14C3.
365 is the smallest number that can be written as a sum of consecutive squares in more than 1 way.
366 is the number of days in a leap year.
367 is the largest number whose square has strictly increasing digits.
368 ???
369 is the number of octominoes.
370 = 33 + 73 + 03.
371 = 33 + 73 + 13.
372 is a hexagonal pyramidal number.
373 is a permutable prime.
374 is the smallest number that can be written as the sum of 3 squares in 8 ways.
375 is a truncated tetrahedral number.
376 is an automorphic number.
377 is the 14th Fibonacci number.
378 ???
379 is a value of n for which one more than the product of the first n primes is prime.
380 ???
381 is a Kaprekar constant in base 2.
382 is the smallest number n with sigma(n) = sigma(n+3).
383 is the number of Hamiltonian graphs with 7 vertices.
384 = 8!!
385 is the number of partitions of 18.
386 ???
387 ???
388 ???
389 ???
390 is the number of partitions of 32 into distinct parts.
391 ???
392 is a Kaprekar constant in base 5.
393 ???
394 ???
395 ???
396 ???
397 ???
398 ???
399 is a value of n for which n!+1 is prime.
400 = 1111 in base 7.
401 is the number of connected planar Eulerian graphs with 9 vertices.
403 is the product of two primes which are reverses of each other.
405 is a pentagonal pyramidal number.
407 = 43 + 03 + 73.
! ! 410 is the smallest number that can written as the sum of 2 distinct primes in 2 ways.
420 is the smallest number divisible by 1 through 7.
426 is a stella octangula number.
427 is a value of n for which n!+1 is prime.
428 has the property that its square is the concatenation of two consecutive numbers.
429 is the 7th Catalan number.
432 = (4) (3)3 (2)2.
434 is the smallest composite value of n for which sigma(n) + 2 = sigma(n+2).
437 has a cube with the last 3 digits the same as the 3 digits before that.
438 = 666 in base 8.
439 is the smallest prime where inserting the same digit between every pair o! ! f digits never yields another prime.
441 is the smallest square which is the sum of 6 consecutive cubes.
442 is the number of planar partitions of 13.
444 is the largest known n for which there is a unique integer solution to a1+…+an=(a1)…(an).
445 has a base 10 representation which is the reverse of its base 9 representation.
446 is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.
448 is the number of 10-iamonds.
449 has a base 3 representation that begins with its base 7 representation.
450 = (5+4)(5+5)(5+0).
451 is the smallest number whose reciprocal has period 10.
454 is the largest number known that cannot be written as a sum of 7 or fewer cubes.
455 = 15C3.
456 is the ! ! number of tournaments with 7 vertices.
461 = 444 + 6 + 11.
462 = 11C5.
465 is a Kaprekar constant in base 2.
466 = 1234 in base 7.
467 has strictly increasing digits in bases 7, 9, and 10.
468 = 3333 in base 5.
469 is the largest known value of n for which n!-1 is prime.
470 has a base 3 representation that ends with its base 6 representation.
471 is the smallest number with the property that its first 4 multiples contain the digit 4.
473 is the largest known number whose square and 4th power use different digits.
475 has a square that is composed of overlapping squares of smaller numbers.
480 is the smallest number which can be written as the difference of 2 squares in 8 ways.
481 is the number of conjugacy classes in the automorphism group of the 10 dimensional hypercube.
482 is a number whose square and cube use different digits.
483 is the last 3-digit string in the decimal expansion of .
484 is a palindromic square number.
487 is the number of Hadamard matrices of order 28.
489 is an octahedral number.
490 is the number of partitions of 19.
495 is the Kaprekar constant for 3-digit numbers.
496 is the 3rd perfect number.
497 is the number of graphs with 8 edges.
499 is the smallest number with the property that its first 12 multiples contain the digit 9.
501 is the number of partitions of 5 items into ordered lists.
503 is the smallest prime which is the sum of the cubes of the first few primes.
504 = 9P3.
505 = 10C5 + 10C0 + 10C5.
510 is the number of binary rooted trees with 14 vertices.
511 = 111111111 in base 2.
512 is the cube! ! of the sum of its digits.
516 is the number of partitions of 32 in which no part occurs only once.
518 = 51 + 12 + 83.
521 is the 13th Lucas number.
525 is a hexagonal pyramida! ! l number.
527 is the smallest number n for which there do not exist 4 smaller numbers so that a1! a2! a3! a4! n! is square.
528 concatenated with its successor is square.
531 is the smallest number with the property that its first 4 multiples contain the digit 1.
535 is a palindrome whose phi(n) is also palindromic.
536 is the number of solutions of the stomachion puzzle.
538 is the 10th meandric number.
540 is divisible by its reverse.
541 is the number of orderings of 5 objects with ties allowed.
543 is a number whose square and cube use different digits.
545 has a base 3 representation that begins with its base 4 representation.
546 undulates in bases 3, 4, and 5.
548 is the maximum number of 9th powers needed to sum to any number.
550 is a pentagonal pyramidal number.
551 is the number of trees with 12 vertices.
552 is the number of prime knots with 11 crossings.
554! ! is the number of self-dual planar graphs with 20 edges.
555 is a repdigit.
559 is a centered cube number.
560 = 16C3.
561 is the smallest Carmichael number.
563 is the largest known Wilson prime.
567 has the property that it and its square together use the digits 1-9 once.
568 is the smallest number whose 7th power can be written as the sum of 7 7th powers.
570 is the product of all the prime palindromic Roman numerals.
572 is the smallest number which has equal numbers of every digit in bases 2 and 3.
573 has the property that its square is the concatenation of two consecutive numbers.
575 is a palindrome that is one less than a square.
576 is the number of 4 x 4 Latin squares.
581 has a base 3 representation that begins with its base 4 representation.
582 is the number of antisymmetric relations on a 5 element set.
583 is the smallest number whose reciprocal has period 26.
585 = 1111 in base 8.
586 is the smallest number that appears in its factorial 6 times.
587 is the smallest number whose sum of digits is larger than that of its cube.
592 evenly divides the sum of it! ! s rotations.
594 = 15 + 29 + 34.
595 is a palindromic triangular number.
598 = 51 + 92 + 83.
607 is the exponent of a Mersenne prime.
610 is the smallest Fibonacci number that begins with 6.
612 is a number whose square and cube use different digits.
614 is the smallest number that can be written as the sum of 3 squares in 9 ways.
617 = 1!2 + 2!2 + 3!2 + 4!2.
619 is a strobogrammatic prime.
620 is the number of sided 7-hexes.
624 is the smallest number with the property that its first 5 multiples contain the digit 2.
625 is an automorphic number.
627 is the number of partitions of 20.
629 evenly divides the sum of its rotations.
630 is the number of degree 13 irreducible polynomials over GF(2).
631 has a base 2 representation that begins with its base 5 representation.
637 = 777 in base 9.
641 is the smallest prime factor of 225+1.
642 is the smallest number with the property that its first 6 multiples contain the digit 2.
645 is the largest ! ! n for which 1+2+3+…+n = 12+22+32+…+k2 for some k.
646 is the number of connected planar graphs with 7 vertices.
648 is the smallest number whose decimal part of its 6th root begins with a permutation of the digits 1-9.
650 is the sum of the first 12 squares.
651 is an nonagonal pentagonal number.
652 is the only known non-perfect number whose number of divisors and sum of smaller divisors are perfect.
653 is the only known prime for which 5 is neither a primitive root or a quadratic residue of 4n2+1.
660 is the order of a non-cyclic simple group.
666 is a palindromic triangular number.
668 is the number of legal pawn moves in chess.
670 is an octahedral number.
671 is a rhombic dodecahedral number.
672 is a multi-perfect number.
675 is the smallest order for which there are 17 groups.
676 is the smallest palindromic square number whose square root is not palindromic.
679 is the smallest number with multiplicative persistence 5.
680 is the smallest tetrahedral number that is also the sum of 2 tetrahedral numbers.
682 = 11C6 + 11C8 + 11C2.
686 is the number of partitions of 35 in which no part occurs only once.
688 is a Friedman number.
689 is the smallest number that can be written as the sum of 3 distinct squares in 9 ways.
694 is the number of partitions of 34 in which no part occurs only once.
696 has a square that is formed by 3 squares that overlap by 1 digit.
697 is a 12-hyperperfect number.
703 is a Kaprekar number.
704 is the number of sided octominoes.
707 is the smallest number whose reciprocal has period 12.
709 is the number of connected planar graphs with 9 edges.
710 is the number of connected graphs with 9 edges.
714 is the smallest number which has equal numbers of every digit in bases 2 and 5.
715 = 13C4.
718 is the ! ! number of unlabeled topologies with 6 elements.
719 is the number of rooted trees with 10 vertices.
720 = 6!
721 is the smallest number which can be written as the difference of two cubes in 2 ways.
724 is the number of diffe! ! rent arrangements of 10 non-attacking queens on an 10×10 chessboard.
726 is a pentagonal pyramidal number.
727 has the property that its square is the concatenation of two consecutive numbers.
728 is the smallest number n where n and n+1 are both products of 5 or more primes.
729 = 36.
730 is the number of connected bipartite graphs with 9 vertices.
731 is the number of planar partitions of 14.
732 = 17 + 26 + 35 + 44 + 53 + 62 + 71.
733 = 7 + 3! + (3!)!
734 is the smallest number that can be written as the sum of 3 distinct non-zero squares in 10 ways.
735 is the smallest number that is the concatenation of its distinct prime factors.
736 is a strong Friedman number.
739 has a base 2 representation that begins with its base 9 representation.
742 is the smallest number that is one more than triple its reverse.
743 is the number of independent sets of the graph of the 4-dimensional hypercube.
746 = 17 + 24 + 36.
750 is the Stirling number of the second kind S(10,8).
752 is the number of conjugacy classes in the automorphism group of the 11 dimensional hypercube.
757 is the smallest number whose reciprocal has a period of 27.
760 is the number of partitions of 37 into distinct parts.
762 is the first decimal digit of where a digit occurs four times in a row.
764 is the number of 8×8 symmetric permutation matrices.
765 is a Kaprekar constant in base 2.
767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution.
773 is the smallest odd number n so that n+2k is composite for all k<n.
777 is a repdigit in bases 6 and 10.
780 = (5+7)(5+8)(5+0).
781 = 11111 in base 5.
784 is the sum of the first 7 cubes.
786 is the largest known n for which 2nCn is not divisible by the square of an odd prime.
787 is a palindromic prime.
788 is the smallest of 6 consecutive numbers divisible by 6 consecutive primes.
791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12.
792 is the number of partitions of 21.
793 is one less than twice its reverse.
794 is the sum of the first 3 6th powers.
797 is the number of functional graphs on 9 vertices.
800 = 2222 in base 7.
802 is the number of isomers of C13H28.
810 is divisible by its reverse.
816 = 18C3.
819 is the smallest number so that it and its successor are both the product of 2 primes and the square of a prime.
820 = 1111 in base 9.
822 is the number of planar graphs with 7 vertices.
835 is the 9th Motzkin number.
836 is a non-palindrome with a palindromic square.
839 has a base 5 representation that begins with its base 9 representation.
840 is the smallest number divisble by 1 through 8.
841 is a square that is also the sum of 2 consecutive squares.
842 is a value of n for which n!! – 1 is prime.
843 is the 14th Lucas number.
844 is the smallest number so that it and the next 4 numbers are all squareful.
846 has the property that its square is the concatenation of two consecutive numbers.
853 is the number of connected graphs with 7 vertices.
854 has the property that it and its square together use the digits 1-9 once.
855 is the smallest number which is the sum of 5 consecutive squares or 2 consecutive cubes.
858 is the smallest palindrome with 4 different prime factors.
864 is the number of partitions of 38 into distinct parts.
866 is the number of sided 10-iamonds.
870 is the sum of its digits and the cube of its digits.
872 is a value of n for which n!+1 is prime.
873 = 1! + 2! + 3! + 4! + 5! + 6!
877 is the 7th Bell number.
880 is the number of 4 x 4 magic squares.
888 has a cube whose digits each occur 3 times.
889 is a Kaprekar constant in base 2.
891 is an octahedral number.
894 has a base 5 representation that begins with its base 9 representation.
895 is a Woodall number.
896 is not the sum of 4 non-zero squares.
899 is the product of twin primes.
900 has a base 5 representation that begins with its base 9 representation.
901 is the sum of the digits of the first 100 positive integers.
906 is the number of perfect graphs with 7 vertices.
907 is the largest n so that Q(n) has class number 3.
912 has exactly the same digits in 3 different bases.
913 has exactly the same digits in 3 different bases.
914 is the number of binary rooted trees with 15 vertices.
919 is the smallest number which is not the difference between palindromes.
922 = 1234 in base 9.
924 is the 6th central binomial coefficient.
925 is the number of partitions of 37 in which no part occurs only once.
927 is the 13th tribonacci number.
929 is a palindromic prime.
936 is a pentagonal pyramidal number.
941 is the smallest number which is the reverse of the sum of its proper substrings.
945 is the smallest odd abundant number.
946 is a hexagonal pyramidal number.
951 is the number of functions from 8 unlabeled points to themselves.
952 = 93 + 53 + 23 + (9)(5)(2).
957 is a value of n for which sigma(n)=sigma(n+1).
960 is the sum of its digits and the cube of its digits.
! ! 961 is a square whose digits can be rotated to give another square.
966 is the Stirling number of the second kind S(8,3).
969 is a tetrahedral palindrome.
976 has a square formed by inserting a block of digits inside itself.
979 is the sum of the first 5 4th powers.
981 is the smallest number that has 5 different partitions into 3 parts with the same product.
982 is the number of partitions of 39 into distinct parts.
985 = 4321 in base 6.
986 = 19 + 28 + 36.
987 is the 16th Fibonacci number.
990 is a triangular number that is the product of 3 consecutive integers.
991 is a permutable prime.
992 is the number of differential structures on the 11-dimensional hypersphere.
993 is the smallest number with the property that its first 15 multiples contain the digit 9.
994 is the smallest number with the property that its first 18 multiples contain the digit 9.
995 has a ! ! square formed by inserting a block of digits inside itself.
996 has a square formed by inserting a block of digits inside itself.
997 is the smallest number with the property that its first 37 multiples contain the digit 9.
998 is the smallest number with the property that its first 55 multiples contain the digit 9.
999 is a Kaprekar number.
1000 = 103.
1001 is the smallest palindromic product of 3 consecutive primes.
1002 is the number of partitions of 22.
1003 has a base 2 representation that ends with its base 3 representation.
1005 is the smallest number whose English name contains all five vowels exactly once.
1006 has a cube that is a concatenation of other cubes.
1009 is the smallest number which is the sum of 3 distinct positive cubes in 2 ways.
1011 has a square that is formed by inserting three 2’s into it.
1012 has a square that is formed by inserting three 4’s into it.
1016 is a stella octangula number.
1019 is a value of n for which one more than the product o! ! f the first n primes is prime.
1021 is a value of n for which one more than the product of the first n primes is prime.
1022 is a Friedman number.
1023 is the smallest number with 4 different digits.
1024 is the smallest number with 11 divisors.
1025 is the smallest number that can be written as the sum of a square and a cube in 4 ways.
1029 is the smallest order for which there are 19 groups.
1031 is the length of the largest repunit that is known to be prime.
1033 = 81 + 80 + 83 + 83.
1035 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
1036 = 4444 in base 6.
1044 is the number of graphs with 7 vertices.
1050 is the Stirling number of the second kind S(8,5).
1052 has the property that placing the last digit first gives 1 more than twice it.
1056 is the area of the smallest non-square rectangle that can be tiled with integer-sided squares.
1067 has exactly the same digits in 3 different bases.
1078 is the number of lattices on 9 unlabeled nodes.
1079 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 15.
1080 is the smallest number with 18 divisors.
1084 is the smallest number whose English name contains all five vowels in order.
1089 is one ninth of its reverse.
1092 is the order of a non-cyclic simple group.
1093 is the smallest Wieferich prime.
1098 = 11 + 0 + 999 + 88.
1099 = 1 + 0 + 999 + 99.
1100 has a base 3 representation that ends with 1100.
1101 has a base 2 representation that ends with 1101.
1104 is a Keith number.
1105 is a rhombic dodecahedral number.
1106 is a truncated tetrahedral number.
1111 is a repdigit.
1112 has a base 3 representation that begins with 1112.
1113 is the number of partitions of 40 into distinct parts.
1116 is the number of polyaboloes with 8 half squares.
1122 = 33C1 + 33C1 + 33C2 + 33C2.
1123 has digits which start the Fibonacci sequence.
1124 is a number whose product of digits is equal to its sum of digits.
1139 has the property that placing the last digit first gives 1 more than 8 times it.
1140 is the smallest number whose divisors contain every digit at least three times.
1141 is the smallest number whose 6th power can be written as the sum of 7 6th powers.
1142 is a number whose product of digits is equal to its sum of digits.
1148 is the number of ways to fold a strip of 9 stamps.
1152 is a highly totient number.
1153 is the smallest number with the property that its first 3 multiples contain the digit 3.
1155 is the product of 4 consecutive primes.
1156 is a square whose digits are non-decreasing.
1161 is the number of degree 14 irreducible polynomials over GF(2).
1165 is the number of conjugacy classes in the automorphism group of the 12 dimensional hypercube.
1166 is a heptagonal pyramidal number.
1167 is the smallest number whose 8th power can be written as the sum of 9 8th powers.
1170 = 2222 in base 8.
1171 has a 4th power containing only 4 different digits.
1183 is the smallest number with the property that its first 4 multiples contain the digit 3.
1184 is an amicable number.
1185 = 11 + 1111 + 8 + 55.
1186 is the number of 11-iamonds.
! ! 1187 = 111 + 111 + 888 + 77.
1189 is the square root of a triangular number.
1193 and its reverse are prime, even if we append or prepend a 3 or 9.
1197 is the smallest number that contains as substrings the maximal prime powers that div! ! ide it.
1200 = 3333 in base 7.
1201 has a square that is formed by inserting three 4’s into it.
1206 is a Friedman number.
1207 is the product of two primes which are reverses of each other.
! ! 1210 is an amicable number.
1214 is a number whose product of digits is equal to its sum of digits.
1215 is the smallest number n where n and n+1 are both products of 6 or more primes.
1222 is a hexagonal pyramidal number.
1224 is the smallest number that can be written as the sum of 4 cubes in 3 ways.
1225 is a hexagonal square triangular number.
1229 is the number of primes less than 10000.
1230 has the property that 17 + 27 + 37 + 07 equals 1230 written in base 8.
1231 has the property that 17 + 27 + 37 + 17 equals 1230 written in base 8.
1233 = 122 + 332.
1234 is the first four positive digits.
1241 is a centered cube number.
1243 is the number of essentially different ways to dissect a 18-gon into 8 quadrilaterals.
1246 is the number of partitions of 38 in which no part occurs only once.
1248 is the smallest number with the property that its first 6 multiples contain the digit 4.
1249 is the number! ! of simplicial polyhedra with 11 vertices.
1255 is a Friedman number.
1260 is the smallest number with 36 divisors.
1275 has a square that is formed by 3 squares that overlap by 1 digit.
1276 = 1111 + 22 + 77 + 66.
1278 = 1111 + 2 + 77 + 88.
1279 is the exponent of a Mersenne prime.
1285 is the number of 9-ominoes.
1287 = 13C5.
1294 is the number of 4 dimensional polytopes with 8 vertices.
1295 = 5555 in base 6.
1296 is a Friedman number.
1297 has a base 2 and base 3 representation that ends with its base 6 representation.
1298 has a base 3 representation that ends with its base 6 representation.
1300 is the sum of the first 4 5th powers.
1301 is the number of trees with 13 vertices.
1306 = 11 + 32 + 03 + 64.
1310 is the smallest number so that it and its neighbors ar! ! e products of three primes.
1320 = 12P3.
1330 = 21C3.
1331 is a cube containing only odd digits.
1332 has a base 2 representation that begins and ends with its base 6 representation.
1333 has a base 2 representation that ends with its base 6 representation.
1334 is a value of n for which sigma(n)=sigma(n+1).
1364 is the 15th Lucas number.
1365 = 15C4.
1366 = 1 + 33 + 666 + 666.
1368 is the number of ways to fold a 3×3 rectangle of stamps.
1369 is a square whose digits are non-decreasing.
1370 = 12 + 372 + 02.
1371 = 12 + 372 + 12.
1376 is the smallest number with the property that it and its neighbors are not cubefree.
1385 is the 8th Euler number.
1386 = 1 + 34 + 8 + 64.
1395 is a vampire number.
1405 is the sum of consecutive squares in 2 ways.
1412 is a number whose product of digits is equal to its sum of digits.
1419 is a Zeisel number.
1421 is a number whose product of digits is equal to its sum of digits.
1426 is the number of partitions of 42 into distinct parts.
1429 is the smallest number whose square has the first 3 digits the same as the next 3 digits.
1430 is the 8th Catalan number.
1435 is a vampire number.
1444 is a square whose digits are non-decreasing.
1448 is the number of 8-hexes.
1449 is a stella octangula number.
1453 = 1111 + 4 + 5 + 333.
1454 = 11 + 444 + 555 + 444.
1455 is the number of subgroups of the symmetric group on 6 symbols.
1458 is the maximum determinant of a 11 x 11 matrix of 0’s and 1’s.
1459 = 11 + 444 + 5 + 999.
1465 has a square that is formed by inserting three 2’s into it.
1467 has the property that e1467 is within 10-8 of an integer.
1469 is an octahedral number.
1470 is a pentagonal pyramidal number.
1476 is the number of graphs with 9 edges.
1477 is a value of n for which n!+1 is prime.
1490 is the 14th tetranacci number.
1494 is the sum of its proper divisors that contain the digit 4.
1500 = (5+1)(5+5)(5+0)(5+0).
1503 is a Friedman number.
1506 is the sum of its proper divisors that contain the digit 5.
1508 is a heptagonal pyramidal number.
1514 is a number whose square and cube use different digits.
1518 is the sum of its proper divisors that contain the digit 5.
1521 is the smallest number that can be writte! ! n as the sum of 4 distinct cubes in 3 ways.
1530 is a vampire number.
1531 appears inside its 4th power.
1533 is a Kaprekar constant in base 2.
1534 = 4321 in base 7.
1536 is not the sum of 4 non-zero squares.
1537 has its largest proper divisor as a substring.
1540 is a tetrahedal triangular number.
1543 = 1111 + 55 + 44 + 333.
1547 is a hexagonal pyramidal number.
1555 is the largest n so that Q(n) has class number 4.
1557 has a square where the first 6 digits alternate.
1562 = 22222 in base 5.
1563 is the smallest number with the property that its first 4 multiples contain the digit 6.
1573 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
1575 is the number of partitions of 24.
1581 is the smallest number whose 8th power contains exactly the same digits as another 8th power.
1584 has a base 3 representation that ends with its base 6 representation.
1585 has a base 3 representation that ends with its base 6 representation.
1586 has a base 3 representation that ends with its base 6 representation.
1595 is the smallest quasi-Carmichael number in base 2.
1597 is the 17th Fibonacci number.
1600 = 4444 in base 7.
1606 is the number of strongly connected digraphs with 4 vertices.
1610 is the number of partitions of 43 into distinct parts.
1624 is the Stirling number of the first kind s(7,3).
1632 is the smallest number with the property that its first 5 multiples contain the digit 6.
1633 is a number whose square and cube use different digits.
1634 = 14 + 64 + 34 + 44.
1636 appears inside its 4th power.
1638 is a harmonic divisor number.
1639 is the number of binary rooted trees with 16 vertices.
1640 = 2222 in base 9.
1650 is the number of connected partial orders on 7 unlabeled elements.
1663 is the number of partitions of 41 in which no part occurs only once.
1666 is the sum of the Roman numerals.
1676 = 11 + 62 + 73 + 64.
1680 is the smallest number with 40 divisors.
1681 is a square and each of its two 2-digit parts is square.
1688 is a truncated tetrahedral number.
1689 is the smallest composite number all of whose divisors (except 1) contain the digit 9.
1692 has a square with the first 3 digits the same as the next 3 digits.
1695 is a rhombic dodecahedral number.
1701 is the Stirling number of the ! ! second kind S(8,4).
1705 is the smallest quasi-Carmichael number in base 4.
1710 is the smallest non-palindrome where it and its reverse are divisible by 19.
1715 = (1) (7)3 (1) (5).
1716 = 13C6.
1722 is a Giuga number.
1728 = 123.
1729 is the smallest number which can be written as the sum of 2 cubes in 2 ways.
1730 is the sum of consecutive squares in 2 ways.
1734 is the sum of its proper divisors that contain the digit 8.
1739 has a base 5 representation that begins with its base 9 representation.
1740 has a base 5 representation that begins with its base 9 representation.
1755 = 3333 in base 8.
1763 is the product of twin primes.
1764 is the Stirling number of the first kind s(7,2).
1770 is the number of conjugacy classes in the automorphism group of the 13 dimensional hypercube.
1771 is a tetrahedral palindrome.
1782 is the smallest number n that is 3 times the sum of all the 2-digit numbers that can be made using the digits of n.
1785 is a Kaprekar constant in base 2.
1787 is the number of different arrangements (up to rotation and reflection) of 12 non-attacking queens on a 12×12 chessboard.
1789! ! is the smallest number with the property that its first 4 multiples contain the digit 7.
1792 is a Friedman number.
1794 has a base 5 representation that begins with its base 9 representation.
1795 has a base 5 representation that begins with its base 9 representation.
1800 is a pentagonal pyramidal number.
1816 is the number of partitions of 44 into distinct parts.
1818 evenly divides the sum of its rotations.
1820 = 16C4.
1822 has a cube that contains only even digits.
1823 has a square with the first 3 digits the same as the next 3 digits.
1824 has a cube that contains only even digits.
1827 is a vampire number.
1828 is the 11th meandric number.
1834 is an octahedral number.
1842 is the number of rooted trees with 11 vertices.
1849 is the smallest composite number all of whose divisors (except 1) contain the digit 4.
1854 is the number of derangements of 7 items.
1858 is the number of isomers of C14H30.
1865 = 12345 in base 6.
1873 is a value of n for which one less than the product of the first n primes is prime.
1875 is the smallest! ! order for which there are 21 groups.
1885 is a Zeisel number.
1890 is the smallest number whose divisors contain every digit at least four times.
1895 is a value of n for which n, 2n, 3n, 4n, 5n, and 6n all use the same number of digits in Roman numerals.
1900 is the largest palindrome in Roman numerals.
1902 has a cube that contains only even digits.
1905 is a Kaprekar constant in base 2.
1908 is the number of self-dual planar graphs with 22 edges.
1911 is a heptagonal pyramidal number.
1913 is prime and contains the same digits as the next prime.
1915 is the number of semigroups of order 5.
1920 is the smallest number that contains more different digits than its cube.
1925 is a hexagonal pyramidal number.
1944 is a member of the Fibonacci-like multiplication series starting with 2 and 3.
1947 is the number of planar partitions of 16.
1953 is a Kaprekar constant in base 2.
1958 is the number of partitions of 25.
1960 is the Stirling number of the first kind s(8,5).
1964 is the number of legal knight moves in chess.
1969! ! is the only known counterexample to a conjecture about modular Ackermann functions.
1980 is the number of ways to fold a 2×4 rectangle of stamps.
1990 is a stella octangula number.
1998 is the largest number that is the sum of its digits and the cube of its digits.
2000 = 5555 in base 7.
2001 has a square with the first 3 digits the same as the next 3 digits.
2002 = 14C5.
2004 has a square with the last 3 digits the same as the 3 digits before that.
2008 is a Kaprekar constant in base 3.
2020 is a curious number.
2024 = 24C3.
2025 is a square that remains square if all its digits are incremented.
2030 ! ! is the smallest number that can be written as a sum of 3 or 4 consecutive squares.
2038 is the number of Eulerian graphs with 9 vertices.
2041 is a 12-hyperperfect number.
2045 is the number of unlabeled partially ordered sets of 7 elements.
2047 is the smallest composite Mersenne number with prime exponent.
2048 is the smallest 11th power (besides 1).
2053 is a value of n for which one less than the product of the first n primes is prime.
2073 is a Genocchi number.
2082 is the sum of its proper divisors that contain the digit 4.
2100 is divisible by its reverse.
2114 is a number whose product of digits is equal to its sum of digits.
2116 has a base 10 representation which is the reverse of its base 7 representation.
2132 is the maximum number of 11th powers needed to sum to any number.
2133 is a 2-hyperperfect number.
2141 is a number whose product of digits is equal to its sum of digits.
2143 is the number of commutative semigroups of order 6.
2147 has a square with the last 3 digits the same as the 3 digits before that.
2164 is the smallest number whose 7th power starts with 5 identical digits.
2176 is the number of prime knots with 12 crossings.
2178 is the only number known which when multiplied by its reverse yields a fourth power.
2182 is the number of degree 15 irreducible polynomials over GF(2).
2184 = 14P3.
2185 is the number of digits of 555.
2186 = 2222222 in ! ! base 3.
2187 is a strong Friedman number.
2188 is the 10th Motzkin number.
2194 is the number of partitions of 42 in which no part occurs only once.
2197 = 133.
2201 is the only non-palindrome known to have a palindromic cube.
2202 is the number of partitions of 43 in which no part occurs only once.
2203 is the exponent of a Mersenne prime.
2207 is the 16th Lucas number.
2208 is a Keith number.
2210 = 47C2 + 47C2 + 47C1 + 47C0.
2213 = 23 + 23 + 133.
2217 has a base 2 representation that begins with its base 3 representation.
2222 is the smallest number divisible by a 1-digit prime, a 2-digit prime, and a 3-digit prime.
2223 is a Kaprekar number.
2244 is a number whose square and cube use different digits.
2255 is an octahedral number.
2257 = 4321 in base 8.
2261 = 2222 + 22 + 6 + 11.
2263 = 2222 + 2 + 6 + 33.
2272 has a cube that is a concatenation of other cubes.
2273 is the number of functional graphs on 10 vertices.
2274 is the sum of its proper divisors that contain the digit 7.
2275 is the sum of the first 6 4th powers.
2281 is the exponent of a Mersenne prime.
2285 is a non-palindrome with a palindromic square.
2295 is the number of self-dual binary codes of length 12.
2300 = 25C3.
2303 is a number whose square and cube use different digits.
2304 is the number of edges in a 9 dimensional hypercube.
2305 has a base 6 representation that ends with its base 8 representation.
2306! ! has a base 6 representation that ends with its base 8 representation.
2307 has a base 6 representation that ends with its base 8 representation.
2308 has a base 6 representation that ends with its base 8 representation.
2309 has a base 6 representation that ends with its base 8 representation.
2310 is the product of the first 5 primes.
2312 has a square with the first 3 digits the same as the next 3 digits.
2318 is the number of connected planar graphs with 10 edges.
2322 is the number of connected graphs with 10 edges.
2328 is the number of groups of order 128.
2331 is a centered cube number.
2336 is the number of sided 11-iamonds.
2340 = 4444 in base 8.
2343 = 33333 in base 5.
2349 is a Friedman number.
2354 = 2222 + 33 + 55 + 44.
2357 is the concatenation of the first 4 primes.
2359 = 2222 + 33 + 5 + 99.
2360 is a hexagonal pyramidal number.
2377 is a value of n for which one less than the product of the first n primes is prime.
2380 = 17C4.
2385 is the smallest number whose 7th power contains exactly the same digits as another 7th power.
2388 is the number of 3-connected graphs with 8 vertices.
2400 = 6666 in base 7.
2401 is the 4th power of the sum of its digits.
2402 has a base 2 representation that begins with its base 7 representation.
2408 is a number whose product of digits is equal to its sum of digits.
2411 is a number whose product of digits is equal to its sum of digits.
2417 has a base 3 representation that begins with its base 7 representation.
2427 = 21 + 42 + 23 + 74.
2431 is the product of 3 consecutive primes.
2434 is the number of legal king moves in chess.
2436 is the number of partitions of 26.
2437 is the smallest number which is not prime when preceded or followed by any digit 1-9.
2445 is a truncated tetrahedral number.
2448 is the order of a non-cyclic simple group.
2450 has a base 3 representation that begins with its base 7 representation.
2460 = 3333 in base 9.
2465 is a Carmichael number.
2467 has a square with the first 3 digits the same as the next 3 digits.
2499 is the number of connected planar Eulerian graphs with 10 vertices.
2500 is a Friedman number.
2501 is a Friedman number.
2502 is a strong Friedman number.
2503 is a Friedman number.
2504 is a Friedman number.
2505 is a Friedman number.
2506 is a Friedman number.
2507 is a Friedman number.
2508 is a Friedman number.
2509 is a Friedman number.
2511 is the smallest number so that it and its successor are both the product of a prime and the 4th power of a prime.
2519 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 12.
2520 is the smallest number divisible by 1 through 10.
2532 = 2222 + 55 + 33 + 222.
2538 has a square with 5/7 of the digits are the same.
2550 is a Kaprekar constant in base 4.
2571 is the smallest number with the property that its first 7 multiples contain the digit 1.
2576 has exactly the same digits in 3 different bases.
2580 is a Keith number.
2584 is the 18th Fibonacci number .
2590 is the number of partitions of 47 into distinct parts.
2592 is a strong Friedman number.
2592 has a base 3 representation that ends with its base 6 representation.
2593 has a base 3 representation that ends with its base 6 representation.
2594 has a base 3 representation that ends with it! ! s base 6 representation.
2600 = 26C3.
2601 is a pentagonal pyramidal number.
2606 is the number of polyhedra with 9 vertices.
2615 is the number of functions from 9 unlabeled points to themselves.
2620 is an amicable number.
2621 = 2222 + 66 + 222 + 111.
2623 = 2222 + 66 + 2 + 333.
2629 is the smallest number whose reciprocal has period 14.
2636 is a non-palindrome with a palindromic square.
2646 is the Stirling number of the second kind S(9,6).
2651 is a stella octangula number.
2657 is a value of n for which one more than the product of the first n primes is prime.
2662 is a palindrome and the 2662nd triangular number is a palindrome.
2665 is the number of conjugacy classes in the automorphism group of the 14 dimensional hypercube.
2673 is the smallest number that can be written as the sum of 3 4th powers in 2 ways.
2680 is the number of different arrangements of 11 non-attacking queens on an 11×11 chessboard.
2683 is the largest n so that Q(n) has class number 5.
2685 is a value of n for which sigma(n)=sigma(n+1).
2694 is the number of ways 22 people around a round table can shake hands in a non-crossing way, up to rotation.
2697 and its product with 5 contain every digit from 1-9 exactly once.
2700 is the product of the first 5 triangular numbers.
2701 is the smallest number n which divides the average of the nth prime and the primes surrounding it.
2728 is a Kaprekar number.
2729 has a square with the first 3 digits the same as the next 3 digits.
2730 = 15P3.
2736 is an octahedral number.
2737 is a strong Friedman number.
2744 = 143.
2745 divides the sum of the primes less than it.
2758 has the property that placing the last digit first gives 1 more than triple it.
2780 = 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81.
2801 = 11111 in base 7.
2802 is the sum of its proper divisors that contain the digit 4.
2805 is the smallest order of a cyclotomic polynomial whose factorization contains 6 as a coefficient.
2821 is a Carmichael number.
2842 is the smallest number with the property that its first 4 multiples contain the digit 8.
2856 is a hexagonal pyramidal number.
2857 is the number of partitions of 44 in which no part occurs only once.
2858 has a square with the first 3 digits the same as the next 3 digits.
2868 has a 4th power containing only 4 different digits.
2872 is the 15th tetranacci number.
2880 is the smallest number that can be written in the form (a2-1)(b2-1) in 3 ways.
2881 has a base 3 representation that ends with its base 6 representation.
2882 has a base 3 representation that ends with its base 6 representation.
2890 is the smallest number in base 9 whose square contains the same digits in the same proportion.
2893 is the number of planar 2-connected graphs with 8 vertices.
2910 is the number of partitions of 48 into distinct parts.
2916 is a Friedman number.
2920 is a heptagonal pyramidal number.
2922 is the sum of its proper divisors that contain the digit 4.
2924 is an amicable number.
2925 = 27C3.
2928 is the number of partitions of 45 in which no part occurs only once.
2931 is the reverse of the sum of its proper substrings.
2938 is the number of binary rooted trees with 17 vertices.
2947 is the smallest number whose 5th power starts with 4 identical digits.
2955 has a 5th power whose digits all occur twice.
2970 is a harmonic divisor number.
2974 is a value of n for which sigma(n)=sigma(n+1).
2996 = 2222 + 99 + 9 + 666.
2997 = 222 + 999 + 999 + 777.
2999 = 2 + 999 + 999 + 999.
3003 is the only number known to appear 8 times in Pascal’s triangle.
3006 has a square with the last 3 digits the same as the 3 digits before that.
3010 is the number of partitions of 27.
3012 is the sum of its proper divisors that contain the digit 5.
3015 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
3024 = 9P4.
3025 is the sum of the first 10 cubes.
3036 is the sum of its proper divisors that contain the digit 5.
3059 is a centered cube number.
3060 = 18C4.
3068 is the number of 10-ominoes that tile the plane.
3069 is a Kaprekar constant in base 2.
3078 is a pentagonal pyramidal number.
3097 is the largest known number n with the property that in every base, there exists a number that is n times the sum of its digits.
3103 = 22C3 + 22C1 + 22C0 + 22C3.
3106 is both the sum of the digits of the 16th and the 17th Mersenne prime.
3110 = 22222 in base 6.
3114 has a square containing only 2 digits.
3120 is the product of the first 6 Fibonacci numbers.
3124 = 44444 in base 5.
3125 is a strong Friedman number.
3126 is a Sierpinski Number of the First Kind .
3135 is the smallest order of a cyclotomic polynomial whose factorization contains 7 as a coefficient.
3136 is a square that remains square if all its digits are decremented.
3137 is the number of planar partitions of 17.
3148 has a square with the first 3 digits the same as the next 3 digits.
3150 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
3156 is the sum of its proper divisors that contain the digit 5.
3159 is the number of trees with 14 vertices.
3160 is the largest known n for which 2n!/(n!)2 does not contain a prime factor less than 12.
3168 has a square whose reverse is also a square.
3174 is the sum of its proper divisors that contain the digit 5.
3178 = 4321 in base 9.
3180 has a base 3 representation that ends with its base 5 representation.
3181 has a base 3 representation that ends with its base 5 representation.
3182 has a base 3 representation that ends with its base 5 representation.
3187 and its product with 8 contain every digit from 1-9 exactly once.
3191 is the smallest number whose reciprocal has period 29.
3210 is the smallest 4-digit number with decreasing digits.
3212 = 37 + 29 + 17 + 29.
3216 is the smallest number with the property that its first 6 multiples contain the digit 6.
3217 is the exponent of a Mersenne prime.
3229 is a value of n for which one more than the product of the first n primes is prime.
3242 has a square with the first 3 digits the same as the next 3 digits.
3248 is the number of legal b! ! ishop moves in chess.
3249 is the smallest square that is comprised of two squares that overlap in one digit.
3254 = 33 + 2222 + 555 + 444.
3259 = 33 + 2222 + 5 + 999.
3264 is the number of partitions of 49 into distinct parts.
3267 = 12345 in base 7.
3276 = 28C3.
3280 = 11111111 in base 3.
3281 is the sum of consecutive squares in 2 ways.
3282 is the sum of its proper divisors that contain the digit 4.
3301 is a value of n for which the nth Fibonacci number begins with the digits in n.
3313 is the smallest prime number where every digit d occurs d times.
3318 has exactly the same digits in 3 different bases.
3320 has! ! a base 4 representation that ends with 3320.
3321 has a base 4 representation that ends with 3321.
3322 has a base 4 representation that ends with 3322.
3323 has a base 4 representation that ends with 3323.
3333 is a repdigit.
3334 is the number of 12-iamonds.
3340 = 3333 + 3 + 4 + 0.
3341 = 3333 + 3 + 4 + 1.
3342 = 3333 + 3 + 4 + 2.
3343 = 3333 + 3 + 4 + 3.
3344 = 3333 + 3 + 4 + 4.
3345 = 3333 + 3 + 4 + 5.
3346 = 3333 + 3 + 4 + 6.
3347 = 3333 + 3 + 4 + 7.
3348 = 3333 + 3 + 4 + 8.
3349 = 3333 + 3 + 4 + 9.
3360 = 16P3.
3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways.
3368 is the number of ways that 8 non-attacking bishops can be placed on a 5×5 chessboard.
3369 is a Kaprekar constant in base 4.
3375 is a Friedman number.
3378 is a Friedman number.
3379 is a number whose square and cube use different digits.
3400 is a truncated tetrahedral number.
3413 = 11 + 22 + 33 + 44 + 55.
3417 is a hexagonal pyramidal number.
3420 is the order of a non-cyclic simple group.
3432 is the 7th central binomia! ! l coefficient.
3435 = 33 + 44 + 33 + 55.
3439 is a rhombic dodecahedral number.
3444 is a stella octangula number.
3465 is the smallest number with the property that its first 5 multiples contain the digi! ! t 3.
3468 = 682 – 342.
3476 is a value of n for which n!! – 1 is prime.
3486 has a square that is formed by 3 squares that overlap by 1 digit.
3489 is the smallest number whose square has the first 3 digits the same as the last 3 digits.
3492 is the number of labeled semigroups of order 4.
3501 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
3510 = 6666 in base 8.
3511 is the largest known Wieferich prime.
3521 = 3333 + 55 + 22 + 111.
3522 is the sum of its proper divisors that contain the digit 7.
3527 is the number of ways to fold a strip of 10 stamps.
3536 is a heptagonal pyramidal number.
3541 is the smallest number whose reciprocal has period 20.
3543 has a cube containing only 3 different digits.
3571 is the 17th Lucas number.
3577 is a Kaprekar constant in base 2.
3584 is not the sum of 4 non-zero squares.
3599 is the product of twin primes.
3600 is a value of n for which n, 2n, 3n, 4n, 5n, 6n, and 7n all use the same number of digits in Roman numerals.
3610 is a pentagonal pyramidal number.
3624 is the smallest number n where n through n+3 are all products of 4 or more primes.
3630 appears inside its 4th power.
3635 has a square with the first 3 digits the same as the next 3 digits.
3645 is the maximum determinant of a 12 x 12 matrix of 0’s and 1’s.
3654 = 29C3.
3655 is the sum of consecutive squares in 2 ways.
3658 is the number of partitions of 50 into distinct parts.
3678 has a square comprised of the digits 1-8.
3684 is a Keith number.
3685 is a strong Friedman number.
3697 is the smallest number in base 6 whose square contains the same digits in the same proportion.
3698 has a square comprised of the digits 0-7.
3718 is the number of partitions of 28.
3721 is the number of partitions of 46 in which no part occurs only once.
3740 is the sum of consecutive squares in 2 ways.
3743 is the number of polyaboloes with 9 half squares.
3745 has a square with the last 3 digits the same as the 3 digits before that.
3747 is the smallest number whose 9th power contains exactly the same digits as another 9th power.
3763 is the largest n so that Q(n) has class number 6.
3784 has a factorization using the same digits as itself.
3786 = 34 + 74 + 8 + 64.
3792 occurs in the middle of its square.
3813 is the number of partitions of 47 in which no part occurs only once.
3825 is a Kaprekar constant in base 2.
3836 is the maximum number of inversions in a permutation of length 7.
3840 = 10!!
3849 has a square with the first 3 digits the same as the next 3 digits.
3861 is the smallest number whose 4th power starts with 5 identical digits.
3864 is a strong Friedman number.
3873 is a Kaprekar constant in base 4.
3876 = 19C4.
3882 is the sum of its proper divisors that contain the digit 4.
3894 is an octahedral number.
3900 has a base 2 representation that is two copies of its base 5 representation concatenated.
3901 has a base 2 representation that ends with its base 5 representation.
3906 = 111111 in base 5.
3911 and its reverse are prime, even if we append or prepend a 3 or 9.
3920 = (5+3)(5+9)(5+2)(5+0).
3925 is a centered cube number.
3926 is the 12th meandric number.
3937 is a Kaprekar constant in base 2.
3956 is the number of conjugacy classes in the automorphism group of the 15 dime! ! nsional hypercube.
3967 is the smallest number whose 12th power contains exactly the same digits as another 12th power.
3969 is a Kaprekar constant in base 2.
3972 is a strong Friedman number.
3977 has its largest proper divisor as a substring.
3985 = 3333 + 9 + 88 + 555.
4000 has a cube that contains only even digits.
4002 has a square with the first 3 digits the same as the next 3 digits.
4006 = 14C4 + 14C0 + 14C0 + 14C6.
4008 has a square with the last 3 digits the same as the 3 digits before that.
4030 is an abundant number that is not the sum of some subset of its divisors.
4032 is the number of connected bipartite graphs with 10 vertices.
4047 is a hexagonal pyramidal number.
4048 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
4051 is the number of partitions of 6 items into ordered lists.
4060 = 30C3.
4062 is the smallest number with the property that its first 8 multiples contain the digit 2.
4080 = 17P3.
4093 is a value of n for which one less than the product of the first n primes is prime.
4095 = 111111111111 in base 2.
4096 is the smallest number with 13 divisors.
4097 is the smallest number (besides 2) that can be written as the sum of two cubes or the sum of two 4th powers.
4099 has a square with the last 3 digits the same as the 3 digits before that.
4100 = 5555 in base 9.
4104 can be written as the sum of 2 cubes in 2 ways.
4106 is a Friedman number.
4112 is a number whose product of digits is equal to its sum of digits.
4121 is a number whose p! ! roduct of digits is equal to its sum of digits.
4128 is the smallest number with the property that its first 10 multiples contain the digit 2.
4140 is the 8th Bell number.
4150 = 45 + 15 + 55 + 05.
4151 = 45 + 15 + 55 + 15.
4152 = 45 + 15 + 55 + 2.
4153 = 45 + 15 + 55 + 3.
4154 = 45 + 15 + 55 + 4.
4155 = 45 + 15 + 55 + 5.
4156 = 45 + 15! ! + 55 + 6.
4157 = 45 + 15 + 55 + 7.
4158 = 45 + 15 + 55 + 8.
4159 = 45 + 15 + 55 + 9.
4160 = 43 + 163 + 03.
4161 = 43 + 163 + 13.
4167 is a Friedman number.
4175 has a square comprised of the digits 0-7.
4181 is the first composite number in the Fibonacci sequence with a prime index.
4186 is a hexagonal, 13-gonal, triangular number.
4187 is the smallest Rabin-Miller pseudoprime with an odd reciprocal period.
4199 is the product of 3 consecutive primes.
4200 is divisible by its reverse.
4207 is the number of cubic graphs with 16 vertices.
4211 is a number whose product of digits is equal to its sum of digits.
4223 is the maximum number of 12th powers needed to sum to any number.
4224 is a palindrome that is one less than a square.
4231 is the number of labeled partially ordered sets with 5 elements.
4233 is a heptagonal pyramidal number.
4243 = 444 + 22 + 444 + 3333.
4253 is the exponent of a Mersenne prime.
4293 has exactly the same digits in 3 different bases.
4297 is a value of n for which one less than the product of the first n primes is prime.
4305 has exactly the same digits in 3 different bases.
4310 has exactly the same digits in 3 different bases.
4312 is the smallest number whose 10th power starts with 7 identical digits.
4320 = (6+4)(6+3)(6+2)(6+0).
4321 is the first four digits in decreasing order.
4332 = 444 + 3333 + 333 + 222.
4335 = 444 + 3333 + 3 + 555.
4336 = 4 + 3333 + 333 + 666.
4339 = 4 + 3333 + 3 + 999.
4342 appears inside its 4th power.
4347 is a heptagonal pentagonal number.
4352 has a cube that contains only even digits.
4356 is two thirds of its reversal.
4357 is the smallest number with the property that its first 5 multiples contain the digit 7.
4364 is a value of n for which sigma(n)=sigma(n+1).
4368 = 16C5.
4381 is a stella octangula number.
4396 = (157)(28) and each digit is contained in the equation exactly once.
4409 is prime, but changing any digit makes it composite.
4423 is the exponent of a Mersenne prime.
4425 is the sum of the first 5 5th powers.
4434 is the sum of its proper divisors that contain the digit 7.
4444 is a repdigit.
4480 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
4489 is a square whose digits are non-decreasing.
4495 = 31C3.
4498 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
4505 is a Zeisel number.
4503 is the largest number that is not the sum of 4 or fewer squares of composites.
4506 is the sum of its proper divisors that contain the digit 5.
4510 = 4444 + 55 + 11 + 0.
4511 = 4444 + 55 + 11 + 1.
4512 = 4444 + 55 + 11 + 2.
4513 = 4444 + 55 + 11 + 3.
4514 = 4444 + 55 + 11 + 4.
4515 = 4444 + 55 + 11 + 5.
4516 = 4444 + 55 + 11 + 6.
4517 = 4444 + 55 + 11 + 7.
4518 = 4444 + 55 + 11 + 8.
4519 = 4444 + 55 + 11 + 9.
4523 has a square in base 2 that is palindromic.
4535 is the number of unlabeled topologies with 7 elements.
4536 is the Stirling number of the first kind s(9,6).
4541 has a square with the first 3 digits the same as the next 3 digits.
4547 is a value of n for which one more than the product of the first n primes is prime.
4548 is the sum of its proper divisors that contain the digit 7.
4552 has a square with the first 3 digits the same as the next 3 digits.
4565 is the number of partitions of 29.
4576 is a truncated tetrahedral number.
4579 is an octahedral number.
4582 is the number of partitions of 52 into distinct parts.
4583 is a value of n for which one less than the product of the first n primes is prime.
4607 is a Woodall number.
4609 = 4444 + 66 + 0 + 99.
4613 is the number of graphs with 10 edges.
4616 has a square comprised of the digits 0-7.
4620 is the largest order of a permutation of 30 or 31 elements.
4624 = 44 + 46 + 42 + 44.
4628 is a Friedman number.
4641 is a rhombic dodecahedral number.
4655 is the number of 10-ominoes.
4665 = 33333 in base 6.
4676 is the sum of the first 7 4th powers.
4681 = 11111 in base 8.
4683 is the number of orderings of 6 objects with ties allowed.
4705 is the sum of consecutive squares in 2 ways.
4713 is a Cullen number.
4734 is the sum of its proper divisors that contain the digit 7.
4750 is a hexagonal pyramidal number.
4752 = (4+4)(4+7)(4+5)(4+2).
4760 is the sum of consecutive squares in 2 ways.
4766 is the number of rooted trees with 12 vertices.
4787 is a value of n for which one more than the product of the first n primes is prime.
4788 is a Keith number.
4793 = 4444 + 7 + 9 + 333.
4804 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
4807 is the smallest quasi-Carmichael number in base 10.
4845 = 20C4.
4851 is a pentagonal pyramidal number.
4862 is the 9th Catalan number.
4863 is th! ! e smallest number that cannot be written as the sum of 273 8th powers.
4866 is the number of partitions of 48 in which no part occurs only once.
4890 is the sum of the first 4 6th powers.
4896 = 18P3.
4900 is the only number which is both square! ! and square pyramidal (besides 1).
4901 has a base 3 representation that begins with its base 7 representation.
4913 is the cube of the sum of its digits.
4920 = 6666 in base 9.
4941 is a centered cube number.
4960 = 32C3.
4967 is the number of partitions of 49 in which no part occurs only once.
4974 is the sum of its proper divisors that contain the digit 8.
5000 is the largest number whose English name does not repeat any letters.
5001 appears inside its 4th power.
5002 has a 4th power containing only 4 different digits.
5005 is the smallest palindromic product of 4 consecutive primes.
5010 has a square with the last 3 digits the sam! ! e as the 3 digits before that.
5016 is a heptagonal pyramidal number.
5020 is an amicable number.
5039 is the number of planar partitions of 18.
5040 = 7!
5041 is the largest square known of the form n!+1.
5050 is the sum of the first 100 integers.
5054 = 555 + 0 + 55 + 4444.
5055 has exactly the same digits in 3 different bases.
5100 is divisible by its reverse.
5104 is the smallest number that can be written as the sum of 3 cubes in 3 ways.
5120 is the number of edges in a 10 dimensional hypercube.
5141 is the only four digit number that is reversed in hexadecimal.
5142 is the sum of its proper divisors that contain the digit 7.
5143 = 555 + 111 + 4444 + 33.
5146 has a base 3 representation that begins with its base 7 representation.
5152 is the number of legal rook moves in chess.
5160 = 5! + (1+6)! + 0.
5161 = 5! + (1+6)! + 1!
5162 = 5! + (1+6)! + 2.
5163 = 5! + (1+6)! + 3.
5164 = 5! + (1+6)! + 4.
5165 = 5! + (1+6)! + 5.
5166 = 5! + (1+6)! + 6.
5167 = 5! + (1+6)! + 7.
5168 = 5! + (1+6)! + 8.
5169 = 5! + (1+6)! + 9.
5174 has a 4th power containing only 4 different digits.
5183 is the product of twin primes.
5187 is the only number n known for which phi(n-1) = phi(n) = phi(n+1).
5200 is divisible by its reverse.
5244 is the sum of consecutive squares in 2 ways.
5258 has a base 8 representation which is the reverse of its base! ! 7 representation.
5269 is the number of binary rooted trees with 18 vertices.
5274 is the sum of its proper divisors that contain the digit 7.
5306 is the smallest number whose 9th power starts with 4 identical digits.
5332 is a Kaprekar constant in base 3.
5340 is an octahedral number.
5346 = (198)(27) and each digit is contained in the equation exactly once.
5349 = 12345 in base 8.
5400 is divisible by its reverse.
5434 is the sum of consecutive squares in 2 ways.
5456 and its reverse are tetrahedral numbers.
5460 is the largest order of a permutation of 32 or 33 elements.
5472 has a base 3 representation that ends with its base 4 representation.
5473 has a base 3 representation that ends with its base 4 representation.
5474 is a stella octangula number.
5477 and its reverse are both one more than a square.
5525 is the smallest number that can be written as the sum of 2 squares in 6 ways.
5530 is a hexagonal pyramidal number.
5536 is the 16th tetranacci number.
5555 is a repdigit.
5564 is an amicable number.
5566 is a pentagonal pyramidal number.
5600 is the number of self-complementary graphs with 13 vertices.
5602 = 22222 in base 7.
5604 is the number of partitions of 30.
5610 is divisible by its reverse.
5616 is the order of a non-cyclic simple group.
5673 is the smallest number whose 6th power starts with 5 identical digits.
5682 is the sum of its proper divisors that contain the digit 4.
5693 = 5555 + 6 + 99 + 33.
5696 = 5555 + 66 + 9 + 66.
5698 is the smallest number whose 8th power starts with 5 identical digits.
5700 is divisible by its reverse.
5718 is the number of partitions of 54 into distinct parts.
5719 is a Zeisel number.
5723 has the property that its square starts with its reverse.
5740 = 7777 in base 9.
5768 is the 16th tribonacci number.
5775 is the product of two different substrings of its digits.
5776 is the square of the last half of its digits.
5777 is the smallest number (besides 1) which is not the sum of a prime and twice a square.
5778 is the largest Lucas number which is also a triangular number.
5784 = 555 + 777 + 8 + 4444.
5786 = 5555 + 77 + 88 + 66.
5795 is a Cullen number.
5796 = (138)(42) and each digit is contained in the equation exa! ! ctly once.
5798 is the 11th Motzkin number.
5814 = 19P3.
5822 is the number of conjugacy classes in the automorphism group of the 16 dimensional hypercube.
5823 and its triple contain every digit from 1-9 exactly once.
5830 is an abundant number that is not the sum of some subset of its divisors.
5832 is the cube of the sum of its digits.
5851 is the only prime so that it, its square, and its cube all have the same sum of digits.
5872 = 5555 + 88 + 7 + 222.
5880 is the Stirling number of the second kind S(10,7).
5890 is a heptagonal pyramidal number.
5904 has a square comprised of the digits 1-8.
5906 is the smallest number which is the sum of 2 rational 4th powers but is not the sum of two integer 4th powers.
5913 = 1! + 2! + 3! + 4! + 5! + 6! + 7!
5915 is the sum of consecutive squares in 2 ways.
5923 is the largest n so that Q(n) has class number 7.
5929 is a square which is also the sum of 11 consecutive squares.
5940 is divisible by its reverse.
5963 = 5555 + 9 + 66 + 333.
5968 has ! ! a square comprised of the digits 0-7.
5972 is the smallest number that appears in its factorial 8 times.
5974 is the number of connected planar graphs with 8 vertices.
5984 = 34C3.
5985 = 21C4.
5986 and its prime factors contain every digit from 1-9 exactly once.
5993 is the largest number known which is not the sum of a prime and twice a square.
5994 is the number of lattices on 10 unlabeled nodes.
5995 is a palindromic triangular number.
5996 is a truncated tetrahedral number.
6001 has a cube that is a concatenation of other cubes.
6003 ! ! has a square with the first 3 digits the same as the next 3 digits.
6006 is the smallest palindrome with 5 different prime factors.
6008 = 14C6 + 14C0 + 14C0 + 14C8.
6012 has a square with the last 3 digits the! ! same as the 3 digits before that.
6014 has a square that is formed by 3 squares that overlap by 1 digit.
6020 is the number of Hamiltonian graphs with 8 vertices.
6021 has a square that is formed by 3 squares that overlap by 1 digit.
6048 is the order of a non-cyclic simple group.
6072 is the order of a non-cyclic simple group.
6077 has a square with the last 3 digits the same as the 3 digits before that.
6084 is the sum of the first 12 cubes.
6095 is a rhombic dodecahedral number.
6099 concatenated with its successor is square.
6102 is the largest number n known where phi(n) is the the reverse of n.
6119 is a centered cube number.
6141 is a Kaprekar constant in base 2.
6144 is not the sum of 4 non-zero squares.
6145 is a Friedman number.
6174 is the Kaprekar constant for 4-digit numbers.
6176 is the last 4-digit sequence to appear in the decimal expansion of .
6181 is an octahedral number.
6188 = 17C5.
6200 is a harmonic divisor number.
6216 has a square with the first 3 digits the same as the next 3 digits.
6220 = 44444 in base 6.
6221 = 666 + 2222 + 2222 + 1111.
6223 = 666 + 2222 + 2 + 3333.
6225 = 666 + 2 + 2 + 5555.
6232 is an amicable number.
6248 is the smallest number with the property that its first 8 multiples contain the digit 4.
6249 is the smallest number with the property that its first 10 multiples contain the digit 4.
6257 is the number of essentially different ways to dissect a 20-gon into 9 quadrilaterals.
6296 has a square with the first 3 digits the same as the next 3 digits.
6300 is divisible by its reverse.
6307 is the largest n s! ! o that Q(n) has class number 8.
6312 is the sum of its proper divisors that contain the digit 5.
6318 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
6348 is a pentagonal pyramidal number.
6368 is an amicable number.
6375 has a square with the first 3 digits the same as the next 3 digits.
6378 is the number of partitions of 55 into distinct parts.
6380 is a value of n for which n!+1 is prime.
6389 is the number of functional graphs on 11 vertices.
6391 is a hexagonal pyramidal number.
6400 is a square whose digits are non-increasing.
6403 has a square with the first 3 digits the same as the last 3 digits.
6404 is a value of n for which n!! – 1 is prime.
6435 = 15C7.
6444 is the smallest number whose 5th power starts with 5 identical digits.
6455 is a strong Friedman number.
6487 is the number of partitions of 51 in which no part occurs only once.
6489 is half again as large as the sum of its proper divisors.
6500 is a number n whose sum of the factorials of its digits is equal to pi(n).
6501 has a square whose reverse is also a square.
6510 is a number n whose sum of the factorials of its digits is equal to pi(n).
6511 is a number n whose sum of the factorials of its digits is equal to pi(n).
6521 is a number n whose sum of the factorials of its digits is equal to pi(n).
6523 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
6524 has the property that its square starts with its reverse.
6526 is the smallest number whose 10th power contains exactly the same digits as another 10th power.
6545 and its reverse are tetrahedral numbers.
6556 is the largest palindrome that can be made using 5 digits and the 4 arithmetic operations.
6560 is the smallest number n where n and n+1 are both products of 7 or more primes.
6561 = 38.
6569 is a value of n for which one less than the product of the first n primes is prime.
6572 is the number of 9-hexes.
6578 is the smallest number which can be written as the sum of 3 4th powers in 2 ways.
6588 is the number of sided 12-iamonds.
6593 = 6 + 5555 + 999 + 33.
6596 has a square comprised of the digits 0-7.
6601 is a Carmichael number.
6603 is a number whose square and cube use different digits.
6611 is a Cullen number.
6620 is the number of 11-ominoes that tile the plane.
6636 has exactly the same digits in 3 different bases.
6643 is the smallest number which is palindromic in bases 2 and 3.
6666 is a repdigit.
6667 is the number of self-dual planar graphs with 24 edges.
6680 = 6666 + 6 + 8 + 0.
6681 = 6666 + 6 + 8 + 1.
6682 = 6666 + 6 + 8 + 2.
6683 = 6666 + 6 + 8 + 3.
6684 = 6666 + 6 + 8 + 4.
6685 = 6666 + 6 + 8 + 5.
6686 = 6666 + 6 + 8 + 6.
6687 = 6666 + 6 + 8 + 7.
6688 = 6666 + 6 + 8 + 8.
6689 = 6666 + 6 + 8 + 9.
6720 = 8P5.
6729 and its double together use each of the digits 1-9 exactly once.
6735 is a stella octangula number.
6742 has a square where the first 6 digits alternate.
6765 is the 20th Fibonacci number.
6769 is the Stirling number of the first kind s(8,4).
6772 = 6666 + 7 + 77 + 22.
6779 = 6666 + 7 + 7 + 99.
6788 is the smallest number with multiplicative persistence 6.
6789 is the largest 4-digit number with increasing digits.
6840 = 20P3.
6842 is the number of partitions of 31.
6859 = 193.
6860 is a heptagonal pyramidal number.
6864 = 6666 + 88 + 66 + 44.
6880 is a vamp! ! ire number.
6888 has a square with 3/4 of the digits are the same.
6889 is a strobogrammatic square.
6912 = (6) (9) (1) (2)7.
6922 is the number of polycubes containing 8 cubes.
6930 is the square root of a triangular number.
6940 is the sum of its proper divisors that contain the digit 3.
6941 has a square with the first 3 digits the same as the last 3 digits.
6942 is the number of labeled topologies with 5 elements.
6951 has exactly the same digits in 3 different bases.
6952 = (1738)(4) and each digit is contained in the equation exactly once.
6953 = 66 + 999 + 5555 + 333.
6966 is! ! the number of planar graphs with 8 vertices.
7014 has a square with the last 3 digits the same as the 3 digits before that.
7106 is an octahedral number.
7108 is the number of partitions of 56 into distinct parts.
7123 is the number of 2-connected graphs with 8 vertices.
7140 is the largest number which is both triangular and tetrahedral.
7145 has a square with the first 3 digits the same as the next 3 digits.
7152 has a square with! ! the first 3 digits the same as the next 3 digits.
7159 has a square with the first 3 digits the same as the next 3 digits.
7161 is a Kaprekar constant in base 2.
7192 is an abundant number that is not the sum of some subset of its divisors.
7200 is a pentagonal pyramidal number.
7230 is the sum of consecutive squares in 2 ways.
7245 appears inside its 4th power.
7254 = (186)(39) and each digit is contained in the equation exactly once.
7272 is a Kaprekar number.
7306 is the smallest number whose 7th power starts with 7 identical digits.
7314 is the smallest number so that it and its successor are both products of 4 primes.
7315 = 22C4.
7318 is the number of functions from 10 unlabeled! ! points to themselves.
7351 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
7360 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
7337 is a hexagonal pyramidal number.
7371 has a base 2 representation that begins with its base 9 representation.
7381 = 11111 in base 9.
7385 is a Keith number.
7422 is the sum of its proper divisors that contain the digit 7.
7429 is the ! ! product of 3 consecutive primes.
7436 is the number of 6×6 alternating sign matrices.
7448 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
7465 = 54321 in base 6.
7471 is a centered cube number.
7490 has a square with the last 3 digits the same as the 3 digits before that.
7491 has a base 8 representation which is the reverse of its base 7 representation.
7494 is the sum of its proper divisors that contain the digit 4.
7496 = 777 + 44 + 9 + 6666.
7512 is the sum of its proper divisors that contain the digit 5.
7525 has a square with the last 3 digits the same as the 3 digits before that.
7532 has a square comprised of the digits 0-7.
7549 is the largest known prime p where no numbers of the form p-n2 are prime.
7560 is the smallest number with 64 divisors.
7574 is the sum of consecutive squares in 2 ways.
7581 is the number of monotone Boolean functions of 5 variables.
7586 = 777 + 55 + 88 + 6666.
7595 is the number of simplicial polyhedra with 12 vertices.
7647 is a Keith number.
7663 is the product of two primes which are reverses of each other.
7665 is a Kaprekar constant in base 2.
7672 = 777 + 6666 + 7 + 222.
7673 is the smallest number with the property that its first 8 multiples contain the digit 3.
7679 = 7 + 6666 + 7 + 999.
7683 is a truncated tetrahedral number.
7693 is a value of n for which the sum of the first n primes is a palindrome.
7698 has a square with the first 3 digits the same as the next 3 digits.
7710 is the number of degree 17 irreducible polynomials over GF(2).
7734 is the sum of its proper divisors that contain the digit 8.
7741 is the number of trees with 15 vertices.
7744 is the only square known with no isolated digits.
7745 and its reverse are both one more than a square.
7770 = 37C3.
7775 = 55555 in base 6.
7776 is a 5th power whose digits are non-increasing.
7777 is a Kaprekar number.
7800 is the order of a non-cyclic simple group.
7810 has the property that its square is the concatenation of two consecutive numbers.
7812 = 222222 in base 5.
7825 is a rhombic dodecahedral number.
7851 = 7777 + 8 + 55 + 11.
7852 = (1963)(4) and each digit is contained in the equation exactly once.
7856 = 7777 + 8 + 5 + 66.
7905 is a Kaprekar constant in base 2.
7909 is a Keith number.
7917 is the number of partitions of 57 into distinct parts.
7920 is the order of the smallest sporadic group.
7928 is a Friedman number.
7931 is a heptagonal pyramidal number.
7936 is the 9th Euler number.
7941 = 7777 + 9 + 44 + 111.
7942 = 7777 + 99 + 44 + 22.
7946 = 7777 + 99 + 4 + 66.
7969 has a square that is formed by 3 squares that overlap by 1 digit.
7980 is the smallest number whose divisors contain every digit at least 7 times.
7993 is one less than twice its reverse.
8000 is the smallest cube which is also the sum of 4 consecutive cubes.
8001 is a Kaprekar constant in base 2.
8004 has a square with the first 3 digits the same as the next 3 digits.
8008 = 16C6.
8016 has a square with the last 3 digits the same as the 3 digits before that.
8026 is the number of planar partitions of 19.
8042 is the largest number known which cannot be written as a sum of 7 or fewer cubes.
8051 is the number of partitions of 52 in which no part occurs only once.
8071 is the number of connected graphs with 11 edges.
8082 has a square comprised of the digits 1-8.
8092 is a Friedman number.
8100 is divisible by its reverse.
8119 is an octahedral number.
8125 is the smallest number that can be written as the sum of 2 squares in 5 ways.
8128 is the 4th perfect number.
8136 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
8176 is a stella octangula number.
8184 has exactly the same digits in 3 different bases.
8190 is a harmonic divisor number.
8191 is a Mersenne prime.
8192 is the smallest 13th power (besides 1).
8200 = 8 + 213 + 0 + 0.
8201 = 8 + 213 + 0 + 1.
8202 = 8 + 213 + 0 + 2.
8203 = 8 ! ! + 213 + 0 + 3.
8204 = 8 + 213 + 0 + 4.
8205 = 8 + 213 + 0 + 5.
8206 = 8 + 213 + 0 + 6.
8207 = 8 + 213 + 0 + 7.
8208 = 84 + 24 + 04 + 84.
8209 = 8 + 213 + 0 + 9.
8221 has a base 3 representation that begins with its base 6 representation.
8226 is the sum of its proper divisors that contain the digit 4.
8281 is the only 4-digit square whose two 2-digit pairs are consecutive.
8283 has a base 8 representation which is the reverse of its base 7 representation.
8303 = 12345 in base 9.
8342 is the number of partitions of 53 in which no part occurs only once.
8349 is the number of partitions of 32.
8372 is a hexagonal pyramidal number.
8375 is the smallest number which has equal numbers of every digit in bases 2 and 6.
8384 is the maximum number of 13th powers needed to sum to any number.
8400 is the number of legal queen moves in chess.
8403 = 33333 in base 7.
8415 is the smallest number which has equal numbers of every digit in bases 3 and 6.
8436 = 38C3.
8461 is the smallest number whose 9th power starts with 5 identical digits.
8470 is the number of conjugacy classes in the automorphism group of the 17 dimensional hypercube.
8486 = 888 + 44 + 888 + 6666.
8510 is a value of n for which the sum of the first n primes is a palindrome.
8515 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
8538 is the sum of its proper divisors that contain the digit 4.
8559 has a square comprised of the digits 1-8.
8562 is the sum of its proper divisors that contain the digit 4.
8568 = 18C5.
8578 appears inside its 4th power.
8586 has exactly the same digits in 3 different bases.
8614 and its prime factors contain every digit from 1-9 exactly once.
8664 = 888 + 6666 + 666 + 444.
8670 is a value of n fo! ! r which n!! – 1 is prime.
8680 has a base 5 representation that ends with its base 7 representation.
8681 has a base 5 representation that ends with its base 7 representation.
8682 has a base 5 representation that ends with its base 7 representation.
8683 has a base 5 representation that ends with its base 7 representation.
8684 has a base 5 representation that ends with its base 7 representation.
8712 is 4 times its reverse.
8714 is the number of ways 24 people around a round table can shake hands in a non-crossing way, up to rotation.
8732 has exactly the same digits in 3 different bases.
8736 is the smallest number that appears in its factorial 10 times.
8753 = 88 + 7777 + 555 + 333.
8758 = 88 + 7777 + 5 + 888.
8763 and its successor have the same digits in their prime factorization.
8772 is the sum of the first 8 4th powers.
8778 is a palindromic triangular number.
8808 is the number of partitions of 58 into distinct parts.
8826 is the sum of its proper divisors that contain the digit 4.
8833 = 882 + 332.
8855 = 23C4.
8888 is a repdigit.
8910 is divisible by its reverse.
8911 is a Carmichael number.
8922 is the sum of its proper divisors that contain the digit 4.
8930 = 8888 + 9 + 33 + 0.
8931 = 8888 + 9 + 33 + 1.
8932 = 8888 + 9 + 33 + 2.
8933 = 8888 + 9 + 33 + 3.
8934 = 8888 + 9 + 33 + 4.
8935 = 8888 + 9 + 33 + 5.
8936 = 8888 + 9 + 33 + 6.
8937 = 8888 + 9 + 33 + 7.
8938 = 8888 + 9 + 33 + 8.
8939 = 8888 + 9 + 33 + 9.
8964 is the smallest number with the proper! ! ty that its first 6 multiples contain the digit 8.
8970 = 8 + 94 + 74 + 0.
8971 = 8 + 94 + 74 + 1.
8972 = 8 + 94 + 74 + 2.
8973 = 8 + 94 + 74 + 3.
8974 = 8 + 94! ! + 74 + 4.
8975 = 8 + 94 + 74 + 5.
8976 = 8 + 94 + 74 + 6.
8977 = 8 + 94 + 74 + 7.
8978 = 8 + 94 + 74 + 8.
8979 = 8 + 94 + 74! ! + 9.
8991 is the smallest number so that it and its successor are both the product of a prime and the 5th power of a prime.
9009 is a centered cube number.
9012 is the sum of its proper divisors that contain the digit 5.
9018 has a square with the last 3 digits the same as the 3 digits before that.
9024 has a square comprised of the digits 1-8.
9025 is a Friedman number.
9072 has a base 2 and base 3 representation that end with its base 6 representation.
9073 has a base 2 and base 3 representation that end with its base 6 representation.
9074 has a base 3 representation that ends with its base 6 representation.
9091 is the only prime known whose reciprocal has period 10.
9093 has a square with the first 3 digits the same as the next 3 digits.
9101 has a square where the first 6 digits alternate.
9104 has a square with the first 3 digits the same as the next 3 digits.
9108 is a heptagonal pyramidal number.
9115 has a base 3 representation that begins with its base 6 representation.
9126 is a pentagonal pyramidal number.
9139 = 39C3.
9174 is the sum of its proper divisors that contain the digit 5.
9189 is the number of sided 10-ominoes.
9216 is a Friedman number.
9224 is an octahedral number.
9233 is the number of different arrangements (up to rotation and reflection) of 13 non-attacking queens on a 13×13 chessboard.
9235 has a square with the first 3 digits the same as the next 3 digits.
9240 = 22P3.
9253 is the smallest number that appears in its factorial 9 times.
9261 is a Friedman number.
9272 is an abundant numbe! ! r that is not the sum of some subset of its divisors.
9330 is the Stirling number of the second kind S(10,3).
9331 = 111111 in base 6.
9349 is the 19th Lucas number.
9350 appears inside its 4th power.
9362 = 22222 in base 8.
9376 is an automorphic number.
9377 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.
9385 is the sum of consecutive squares in 2 ways.
9386 = 99 + 333 + 8888 + 66.
9391 has a square with the first 3 digits the same as the last 3 digits.
9408 is the number of reduced 6 x 6 Latin squares.
9436 is the smallest number whose 15th power contains exactly the same digits as another 15th power.
9444 has a square with the first 3 digits the same as the next 3 digits.
9451 is the number of binary rooted trees with 19 vertices.
9468 is the sum of its proper divisorsproper divisors that contain the digit 7.
9474 = 94 + 44 + 74 + 44.
9477 is the maximum determinant of a 13 x 13 matrix of 0’s and 1’s.
9496 is the number of 10×10 symmetric permutation matrices.
9500 is a hexagonal pyrami! ! dal number.
9563 = 9 + 5555 + 666 + 3333.
9568 = 9 + 5 + 666 + 8888.
9608 is the number of digraphs with 5 vertices.
9615 is the smallest number whose cube starts with 5 identical digits.
9625 has a square formed by inserting a block of digits inside itself.
9653 = 99 + 666 + 5555 + 3333.
9658 = 99 + 666 + 5 + 8888.
9660 is a truncated tetrahedral number.
9682 is a value of n for which! ! n!! – 1 is prime.
9689 is the exponent of a Mersenne prime.
9726 is the smallest number in base 5 whose square contains the same digits in the same proportion.
9784 is the number of 2 state Turing machines which halt.
9789 is the smallest number that appears in its factorial 11 times.
9792 is the number of partitions of 59 into distinct parts.
9801 is 9 times its reverse.
9809 is a stella octangula number.
9828 is the orde! ! r of a non-cyclic simple group.
9831 has a base 6 representation which is the reverse of its base 5 representation.
9841 = 111111111 in base 3.
9855 is a rhombic dodecahedral number.
9862 is the number of knight’s tours on a 6 x 6 chess board.
9876 is the largest 4-digit number with different digits.
9880 = 40C3.
9901 is the only prime known whose reciprocal has period 12.
9941 is the exponent of a Mers! ! enne prime.
9973 is the largest 4-digit prime.
9976 has a square formed by inserting a block of digits inside itself.
9988 is the number of prime knots with 13 crossings.
9995 has a square formed by inserting a block of digits inside itself.
9996 has a square formed by inserting a block of digits inside itself.
9999 is a Kaprekar number.

Its simply an awesome collection ! Who ever reads this pass this on to your friends. Let them know the significance of each number 🙂

1 is the multiplicative identity.

2 is the only even prime.

3 is the ! ! number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar maps.

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of integer-sided rectangles that tile a rectangle so that no 2 rectangles share a common length.

8 is the largest cube in the Fibonacci sequence.

9 is the maximum number of cubes that are needed to sum to any positive integer.

10 is the base of our number system.

11 is the largest known multiplicative persistence.

12 is the smallest abundant number.

13 is the number of Archimedian solids.

14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.

15 is the smallest composite number n with the property that there is only one group of order n.

16 is the only number of the form xy=yx with x and y different integers.

17 is the number of wallpaper groups.

18 is the only number that is twice the sum of its digits.

19 is the maximum number of 4th powers needed to sum to any number.

20 is the number of rooted trees with 6 vertices.

21 is the smallest number of distinct squares needed to tile a square.

22 is the number of partitions of 8.

23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

24 is the largest number divisible by all numbers less than its square root.

25 is the smallest square that can be written as a sum of 2 squares.

26 is the only number to be directly between a square and a cube.

27 is the largest number that is the sum of the digits of its cube.

28 is the 2nd perfect number.

29 is the 7th Lucas number.

30 is the largest number with the property that all smaller numbers relatively prime to it are prime.

31 is a Mersenne prime.

32 is the smallest 5th power (besides 1).

33 is the largest number that is not a sum of distinct triangular numbers.

34 is the smallest number with the property that it and its neighbors have the same number of divisors.

35 is the number of hexominoes.

36 is the smallest number (besides 1) which is both square and triangular.

37 is the maximum number of 5th powers needed to sum to any number.

38 is the last Roman numeral when written lexicographically.

39 is the smallest number which has 3 different partitions into 3 parts with the same product.

40 is the only number whose letters are in alphabetical order.

41 is the smallest number that is not of the form |2x – 3y|.

42 is the 5th Catalan number.

43 is the number of sided 7-iamonds.

44 is the number of derangements of 5 items.

45 is a Kaprekar number.

46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.

47 is the largest number of cubes that cannot tile a cube.

48 is the smallest number with 10 divisors.

49 is the smallest number with the property that it and its neighbors are squareful.

50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.

51 is the 6th Motzkin number.

52 is the 5th Bell number.

53 is the only two digit number that is reversed in hexadecimal.

54 is the smallest number that can be written as the sum of 3 squares in 3 ways.

55 is the largest triangula! ! r number in the Fibonacci sequence.

56 is the number of reduced 5 x 5 Latin squares.

57 = 111 in base 7.

58 is the number of commutative semigroups of order 4.

59 is the smallest number whose 4th power is of the form a4+b4-c4.

60 is the smallest number divisible by 1 through 6.

61 is the 6th Euler number.

62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways.

63 is the number of partially ordered sets of 5 elements.

64 is the smallest number with 7 divisors.

65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.

66 is the number of 8-iamonds.

67 is the smallest number which is palindromic in bases 5 and 6.

68 is the last 2-digit string to appear in the decimal expansion of .

69 has the property that n2 and n3 together contain each digit once.

70 is the smallest abundant number that is not the sum of some subset of its divisors.

71 divides the sum of the primes less than it.

72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.

73 is the smallest number (besides 1) which is one less than twice its reverse.

74 is the number of different non-Hamiltonian polyhedra with minimum number of vertices.

75 is the number of orderings of 4 objects with ties allowed.

76 is an automorphic number.

77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.

78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.

79 is a permutable prime.

80 is the smallest number n where n and n+1 are both products of 4 or more primes.

81 is the square of the sum of its digits.

82 is the number of 6-hexes.

83 is the number of zero-less pandigital squares.

84 is the largest order of a permutation of 14 elements.

85 is the largest n for which 12+22+32+…+n2 = 1+2+3+…+m has a solution.

86 = 222 in base 6.

87 is the sum of the squares of the first 4 primes.

88 is the only number known whose square has no isolated digits.

89 = 81 + 92

90 is the number of degrees in a right angle.

91 is the smallest pseudoprime in base 3.

92 is the number of different arrangements of 8 non-attacking queens on an 8×8 chessboard.

93 = 333 in base 5.

94 is a Smith number.

95 is the number of planar partitions of 10.

96 is the smallest number that can be written as the difference of 2 squares in 4 ways.

97 is the smallest number with the property that its first 3 multiples contain the digit 9.

98 is the smallest number with the property that its first 5 multiples contain the digit 9.

99 is a Kaprekar number.

100 is the smallest square which is also the sum of 4 consecutive cubes.

101 is the number of partitions of 13.

102 is the smallest number with three different digits.

103 has the property that placing the last digit first gives 1 more than triple it.

104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex.

105 is the largest number n known with the property that n – 2k ! ! is prime for k>1.

106 is the number of trees with 10 vertices.

107 is the exponent of a Mersenne prime.

108 is 3 hyperfactorial.

109 is the smallest number w! ! hich is palindromic in bases 5 and 9.

110 is the smallest number that is the product of two different substrings.

111 is the smallest possible magic constant of a 3 x 3 magic square of distinct primes.

112 is the side of the smallest square that can be tiled with distinct integer-sided squares.

113 is a permutable prime.

114 = 222 in base 7.

115 is the number of rooted trees with 8 vertices.

116 is a value of n for which n!+1 is prime.

117 is the smallest possible value of the longest edge in a Heronian Tetrahedron.

118 is the smallest number that has 4 different partitions into 3 parts with the same product.

119 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 8.

120 is the smallest number to appear 6 times in Pascal’s triangle.

121 is the only square known of the form 1+p+p2+p3+p4, where p is prime.

122 is the smallest number n>1 so that n concatenated with n-1 0’s concatenated with the reverse of n is prime.

123 is the 10th Lucas number.

124 is the smallest number with the property that its first 3 multiples contain the digit 2.

125 is the only number known that contains all its proper divisors as proper substrings.

126 = 9C4.

127 is a Mersenne prime.

128 is the largest number which is not the sum of distinct squares.

129 is the smallest number that can be written as the sum of 3 squares in 4 ways.

130 is the number of functions from 6 unlabeled points to themselves.

131 is a permutable prime.

132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.

133 is the smallest number n for which the sum of the proper divisors of n divides phi(n).

134 = 8C1 + 8C3 + 8C4.

! ! 135 = 11 + 32 + 53.

136 is the sum of the cubes of the digits of the sum of the cubes of its digits.

137 is the smallest prime with 3 distinct digits that remains prime if one of its digits is removed.

138 is the smallest possible product of 3 primes, one of which is the concatenation of the other two.

139 is the number of unlabeled topologies with 5 elements.

140 is the smallest harmonic divisor number.

141 is a Cullen number.

142 is the number of planar graphs with 6 vertices.

143 is the smallest quasi-Carmichael number in base 8.

144 is the largest square in the Fibonacci sequence.

145 = 1! + 4! + 5!

146 = 222 in base 8.

147 is the number of sided 6-hexes.

148 is the number of perfect graphs with 6 vertices.

149 is the concatenation of the first 3 positive squares.

150 is the smallest n for which n + n times the nth prime is square.

151 is a palindromic prime.

152 has a square comprised of the digits 0-4.

153 = 13 + 53 + 33.

154 is the smallest number which is palindromic in bases 6, 8, and 9.

155 is the sum of the primes between its smallest and largest prime factor.

156 is the number of graphs with 6 vertices.

157 is the largest number kn! ! own whose square contains the same digits as its successor.

158 is the number of planar partitions of 11.

159 is the number of isomers of C11H24.

160 is the number of 9-iamonds.

161 is a hexagonal pyramidal number.

162 is the smallest number that can be written as the sum of of 4 positive squares in 9 ways.

163 is the largest Heegner Number.

164 is the smallest number which is the concatenation of squares in two different ways.

165 = 11C3.

166 is the number of monotone Boolean functions of 4 variables.

167 is the smallest number whose 4th power begins with 4 identical digits

168 is the size of the smallest non-cyclic simple group which is not an alternating group.

169 is a square whose digits are non-decreasing.

170 is the smallest number n for which phi(n) and sigma(n) are both square.

171 has the same number of digits in Roman numerals as its cube.

172 = 444 in base 6.

173 has a square containing only 2 digits.

174 is the smallest number that can be written as the sum of of 4 positive distinct squares in 6 ways.

175 = 11 + 72 + 53.

176 is an octagonal pentagonal number.

177 is the number of graphs with 7 edges.

178 has a cube with the same digits as another cube.

179 has a square comprised of the digits 0-4.

180 is the total number of degrees in a triangle.

181 is a strobogrammatic prime.

182 is the number of connected bipartite graphs with 8 vertices.

183 is the smallest number n so that n concatenated with n+1 is square.

184 is a Kaprekar constant in base 3.

185 is the number of conjugacy classes in the automorphism group of the 8 dimensional hypercube.

186 is the number of degree 11 irreducible polynomials over GF(2).

187 is the smallest quasi-Carmichael number in base 7.

188 is the number of semigroups of order 4.

189 is a Kaprekar constant in base 2.

190 is th! ! e largest number with the property that it and its ditinct prime factors are palindromic in Roman numerals.

191 is a palindromic prime.

192 is the smallest number with 14 divisors.

193 is the only known odd prime n for which 2 is! ! not a primitive root of 4n2+1.

194 is the smallest number that can be written as the sum of 3 squares in 5 ways.

195 is the smallest value of n such that 2nCn is divisible by n2.

196 is the smallest number that is not known to reach a palindrome when repeatedly added to its reverse.

197 is a Keith number.

198 = 11 + 99 + 88.

199 is the 11th Lucas number.

200 is the smallest number which can not be made prime by changing one of its digits.

201 is a Kaprekar constant in base 4.

202 has a cube that contains only even digits.

203 is the 6th Bell number.

204 is the square root of a triangular number.

205 is the largest number which can not be writen as the sum of distinct primes of the form 6n+1.

206 is the smallest number that can be written as the sum of of 3 positive distinct squares in 5 ways.

207 has a 4th power where the first half of the digits are a permutation of the last half of the digits.

208 is the 10th tetranacci number.

209 is the smallest quasi-Carmichael number in base 9.

210 is the product of the first 4 primes.

211 has a cube containing only 3 different digits.

212 has a square with 4/5 of the digits are the same.

213 is a number whose product of digits is equal to its sum of digits.

214 is a value of n for which n!! – 1 is prime.

215 = 555 in base 6.

216 is th! ! e smallest cube that can be written as the sum of 3 cubes.

217 is a Kaprekar constant in base 2.

218 is the number of digraphs with 4 vertices.

219 is the number of space groups, not including handedness.

220 is the smallest amicable number.

221 is the number of Hamiltonian planar graphs with 7 vertices.

222 is the number of lattices on 10 unlabeled nodes.

223 is the smallest prime which will nor remain prime if one of its digits is changed.

224 is not the sum of 4 non-zero squares.

225 is an octagonal square number.

226 ???

227 is the number of connected planar graphs with 8 edges.

228 = 444 in base 7.

229 is the smallest prime that remains prime when added to its reverse.

230 is the number of space groups, including handedness.

231 is the number of partitions of 16.

232 is the number of 7×7 symmetric permutation matrices.

233 is the smallest number with the property that it and its neighbors can be written as a sum of 2 squares.

234 ???

235 is the number of trees with 11 vertices.

236 is the number of Hamiltonian circuits of a 4×8 rectangle.

237 is the smallest number with the property that its first 3 multiples contain the digit 7.

238 is the number of connected partial orders on 6 unlabeled elements.

239 is the largest number that cannot be written as a sum of 8 or fewer cubes.

240 is the smallest number with 20 divisors.

241 ???

242 is the smallest number n where n through n+3 all have the same number of divisors.

243 = 35.

244 is the smallest number (besides 2) that can be written as the sum of 2 squares or the sum of 2 5th powers.

245 is a stella octangula number.

246 = 9C2 + 9C4 + 9C6.

247 is the smallest possible difference between two integers that together contain each digit exactly once.

248 is the smallest number n>1 for which the arithmetic, geometric, and harmonic means of phi(n) and sigma(n) are all integers.

249 ???

250 ???

251 is the smallest number that can be written as the sum of 3 cubes in 2 ways.

252 is the 5th central binomial coefficient.

253 is the smalles! ! t non-trivial triangular star number.

254 is the smallest composite number all of whose divisors (except 1) contain the digit 2.

255 = 11111111 in base 2.

256 is the smallest 8th power (besides 1).

257 is a Fermat prime.

258 ???

259 = 1111 in base 6.

260 is the number of ways that 6 non-attacking bishops can be placed on a 4×4 chessboard.

261 is the number of essentially different ways to dissect a 16-gon into 7 quadrilaterals.

262 is the 9th meandric number.

263 is the largest known prime whose square is strobogrammatic.

264 is the largest known number whose square is undulating.

265 is the number of derangements of 6 items.

266 is the Stirling number of the second kind S(8,6).

267 is the number of planar partitions of 12.

268 is the smallest number whose product of digits is 6 times the sum of its digits.

269 ???

270 is a harmonic divisor number.

271 is the smallest prime p so that p-1 and p+1 are divisible by cubes.

272 is the 7th Euler number.

273 = 333 in base 9.

274 is the Stirling number of the first kind s(6,2).

275 is the number of partitions of 28 in which no part occurs only once.

276 is the sum of the first 3 5th powers.

277 ???

278 ???

279 is the maximum number of 8th powers needed to sum to any number.

280 is the number of ways 18 people around a round table can shake hands in a non-crossing way, up to rotation.

281 is the sum of the first 14 primes.

282 is the sum of its proper divisors that contain the digit 4.

283 = 25 + 8 + 35.

284 is an amicable number.

285 is the number of binary rooted trees with 13 vertices.

286 is the number of rooted trees with 9 vertices.

287 is the sum of consecutive primes in 3 different ways.

288 is the smallest non-palindrome non-square that when multiplied by its reverse is a square.

289 is a Friedman number.

290 has a base 3 representation that ends with its base 6 representation.

291 is the number of functional graphs on 8 vertices.

292 is the number of ways to make change for a dollar.

293 ???

294 is the number of planar 2-connected graphs with 7 vertices.

295 ???

296 is the number of partitions of 30 into distinct parts.

297 is a Kaprekar number.

298 ???

299 ???

300 is the largest possible score in bowling.

301 is a 6-hyperperfect number.

302 is the number of acyclic digraphs with 5 vertices.

303 has a cube that is a concatenation of other cubes.

304 ???

305 ???

306 ???

307 is a non-palindrome with a palindromic square.

308 is a heptagonal pyramidal number.

309 is smallest value of n for which sigma(n-1) + sigma(n+1) = sigma(2n).

310 = 1234 in base 6.

311 is a permutable prime.

312 = 2222 in base 5.

313 is a palindromic prime.

314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways.

315 = (4+3)(4+1)(4+5).

316 ???

317 is a value of n for which one less than the product of the first n primes is prime.

318 is the number of unlabeled partially ordered sets of 6 elements.

319 is the smallest number with the property that the partition with the largest product does not have a maximum number of parts.

320 is the maximum determinant of a 10 x 10 matrix of 0’s and 1’s.

321 is a number whose product of digits is equal to its sum of digits.

322 is the 12th Lucas number.

323 is the product of twin primes.

324 is the largest possible product of positive integers with sum 16.

325 is a 3-hyperperfect number.

326 ???

327 and its double and triple together contain every digit from 1-9 exactly once.

328 concatenated with its successor is square.

329 ???

330 = 11C4.

331 ???

332 ???

333 is the number of 7-hexes.

334 ???

335 is the number of degree 12 irreducible polynomials over GF(2).

336 = 8P3.

337 is a permutable prime.

338 ???

339 ???

340 is a value of n for which n!+1 is prime.

341 is the smallest pseudoprime in base 2.

342 = 666 in base 7.

343 is a strong Friedman number.

344 is an octahedral number.

345 is half again as large as the sum of its proper divisors.

346! ! ???

347 is a Friedman number.

348 is the smallest number whose 5th power contains exactly the same digits as another 5th power.

349 ???

350 is the Stirling number of the second kind S(7,4).

351 is the smallest number n where n, n+1, and n+2 are all products of 4 or more primes.

352 is the number of different arrangements of 9 non-attacking queens on an 9×9 chessboard.

353 is the smallest number whose 4th power can be written as the sum of 4 4th powers.

354 is the sum of the first 4 4th powers.

355 is the number of labeled topologies with 4 elements.

356 ???

357 has a base 3 representation that ends with its base 7 representation.

358 has a base 3 representation that ends with its base 7 representation.

359 has a base 3 representation that ends with its base 7 representation.

360 is the number of degrees in a circle.

361 ???

362 and its double and triple all use the same number of digits in Roman numerals.

363 ???

364 = 14C3.

365 is the smallest number that can be written as a sum of consecutive squares in more than 1 way.

366 is the number of days in a leap year.

367 is the largest number whose square has strictly increasing digits.

368 ???

369 is the number of octominoes.

370 = 33 + 73 + 03.

371 = 33 + 73 + 13.

372 is a hexagonal pyramidal number.

373 is a permutable prime.

374 is the smallest number that can be written as the sum of 3 squares in 8 ways.

375 is a truncated tetrahedral number.

376 is an automorphic number.

377 is the 14th Fibonacci number.

378 ???

379 is a value of n for which one more than the product of the first n primes is prime.

380 ???

381 is a Kaprekar constant in base 2.

382 is the smallest number n with sigma(n) = sigma(n+3).

383 is the number of Hamiltonian graphs with 7 vertices.

384 = 8!!

385 is the number of partitions of 18.

386 ???

387 ???

388 ???

389 ???

390 is the number of partitions of 32 into distinct parts.

391 ???

392 is a Kaprekar constant in base 5.

393 ???

394 ???

395 ???

396 ???

397 ???

398 ???

399 is a value of n for which n!+1 is prime.

400 = 1111 in base 7.

401 is the number of connected planar Eulerian graphs with 9 vertices.

403 is the product of two primes which are reverses of each other.

405 is a pentagonal pyramidal number.

407 = 43 + 03 + 73.

! ! 410 is the smallest number that can written as the sum of 2 distinct primes in 2 ways.

420 is the smallest number divisible by 1 through 7.

426 is a stella octangula number.

427 is a value of n for which n!+1 is prime.

428 has the property that its square is the concatenation of two consecutive numbers.

429 is the 7th Catalan number.

432 = (4) (3)3 (2)2.

434 is the smallest composite value of n for which sigma(n) + 2 = sigma(n+2).

437 has a cube with the last 3 digits the same as the 3 digits before that.

438 = 666 in base 8.

439 is the smallest prime where inserting the same digit between every pair o! ! f digits never yields another prime.

441 is the smallest square which is the sum of 6 consecutive cubes.

442 is the number of planar partitions of 13.

444 is the largest known n for which there is a unique integer solution to a1+…+an=(a1)…(an).

445 has a base 10 representation which is the reverse of its base 9 representation.

446 is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.

448 is the number of 10-iamonds.

449 has a base 3 representation that begins with its base 7 representation.

450 = (5+4)(5+5)(5+0).

451 is the smallest number whose reciprocal has period 10.

454 is the largest number known that cannot be written as a sum of 7 or fewer cubes.

455 = 15C3.

456 is the ! ! number of tournaments with 7 vertices.

461 = 444 + 6 + 11.

462 = 11C5.

465 is a Kaprekar constant in base 2.

466 = 1234 in base 7.

467 has strictly increasing digits in bases 7, 9, and 10.

468 = 3333 in base 5.

469 is the largest known value of n for which n!-1 is prime.

470 has a base 3 representation that ends with its base 6 representation.

471 is the smallest number with the property that its first 4 multiples contain the digit 4.

473 is the largest known number whose square and 4th power use different digits.

475 has a square that is composed of overlapping squares of smaller numbers.

480 is the smallest number which can be written as the difference of 2 squares in 8 ways.

481 is the number of conjugacy classes in the automorphism group of the 10 dimensional hypercube.

482 is a number whose square and cube use different digits.

483 is the last 3-digit string in the decimal expansion of .

484 is a palindromic square number.

487 is the number of Hadamard matrices of order 28.

489 is an octahedral number.

490 is the number of partitions of 19.

495 is the Kaprekar constant for 3-digit numbers.

496 is the 3rd perfect number.

497 is the number of graphs with 8 edges.

499 is the smallest number with the property that its first 12 multiples contain the digit 9.

501 is the number of partitions of 5 items into ordered lists.

503 is the smallest prime which is the sum of the cubes of the first few primes.

504 = 9P3.

505 = 10C5 + 10C0 + 10C5.

510 is the number of binary rooted trees with 14 vertices.

511 = 111111111 in base 2.

512 is the cube! ! of the sum of its digits.

516 is the number of partitions of 32 in which no part occurs only once.

518 = 51 + 12 + 83.

521 is the 13th Lucas number.

525 is a hexagonal pyramida! ! l number.

527 is the smallest number n for which there do not exist 4 smaller numbers so that a1! a2! a3! a4! n! is square.

528 concatenated with its successor is square.

531 is the smallest number with the property that its first 4 multiples contain the digit 1.

535 is a palindrome whose phi(n) is also palindromic.

536 is the number of solutions of the stomachion puzzle.

538 is the 10th meandric number.

540 is divisible by its reverse.

541 is the number of orderings of 5 objects with ties allowed.

543 is a number whose square and cube use different digits.

545 has a base 3 representation that begins with its base 4 representation.

546 undulates in bases 3, 4, and 5.

548 is the maximum number of 9th powers needed to sum to any number.

550 is a pentagonal pyramidal number.

551 is the number of trees with 12 vertices.

552 is the number of prime knots with 11 crossings.

554! ! is the number of self-dual planar graphs with 20 edges.

555 is a repdigit.

559 is a centered cube number.

560 = 16C3.

561 is the smallest Carmichael number.

563 is the largest known Wilson prime.

567 has the property that it and its square together use the digits 1-9 once.

568 is the smallest number whose 7th power can be written as the sum of 7 7th powers.

570 is the product of all the prime palindromic Roman numerals.

572 is the smallest number which has equal numbers of every digit in bases 2 and 3.

573 has the property that its square is the concatenation of two consecutive numbers.

575 is a palindrome that is one less than a square.

576 is the number of 4 x 4 Latin squares.

581 has a base 3 representation that begins with its base 4 representation.

582 is the number of antisymmetric relations on a 5 element set.

583 is the smallest number whose reciprocal has period 26.

585 = 1111 in base 8.

586 is the smallest number that appears in its factorial 6 times.

587 is the smallest number whose sum of digits is larger than that of its cube.

592 evenly divides the sum of it! ! s rotations.

594 = 15 + 29 + 34.

595 is a palindromic triangular number.

598 = 51 + 92 + 83.

607 is the exponent of a Mersenne prime.

610 is the smallest Fibonacci number that begins with 6.

612 is a number whose square and cube use different digits.

614 is the smallest number that can be written as the sum of 3 squares in 9 ways.

617 = 1!2 + 2!2 + 3!2 + 4!2.

619 is a strobogrammatic prime.

620 is the number of sided 7-hexes.

624 is the smallest number with the property that its first 5 multiples contain the digit 2.

625 is an automorphic number.

627 is the number of partitions of 20.

629 evenly divides the sum of its rotations.

630 is the number of degree 13 irreducible polynomials over GF(2).

631 has a base 2 representation that begins with its base 5 representation.

637 = 777 in base 9.

641 is the smallest prime factor of 225+1.

642 is the smallest number with the property that its first 6 multiples contain the digit 2.

645 is the largest ! ! n for which 1+2+3+…+n = 12+22+32+…+k2 for some k.

646 is the number of connected planar graphs with 7 vertices.

648 is the smallest number whose decimal part of its 6th root begins with a permutation of the digits 1-9.

650 is the sum of the first 12 squares.

651 is an nonagonal pentagonal number.

652 is the only known non-perfect number whose number of divisors and sum of smaller divisors are perfect.

653 is the only known prime for which 5 is neither a primitive root or a quadratic residue of 4n2+1.

660 is the order of a non-cyclic simple group.

666 is a palindromic triangular number.

668 is the number of legal pawn moves in chess.

670 is an octahedral number.

671 is a rhombic dodecahedral number.

672 is a multi-perfect number.

675 is the smallest order for which there are 17 groups.

676 is the smallest palindromic square number whose square root is not palindromic.

679 is the smallest number with multiplicative persistence 5.

680 is the smallest tetrahedral number that is also the sum of 2 tetrahedral numbers.

682 = 11C6 + 11C8 + 11C2.

686 is the number of partitions of 35 in which no part occurs only once.

688 is a Friedman number.

689 is the smallest number that can be written as the sum of 3 distinct squares in 9 ways.

694 is the number of partitions of 34 in which no part occurs only once.

696 has a square that is formed by 3 squares that overlap by 1 digit.

697 is a 12-hyperperfect number.

703 is a Kaprekar number.

704 is the number of sided octominoes.

707 is the smallest number whose reciprocal has period 12.

709 is the number of connected planar graphs with 9 edges.

710 is the number of connected graphs with 9 edges.

714 is the smallest number which has equal numbers of every digit in bases 2 and 5.

715 = 13C4.

718 is the ! ! number of unlabeled topologies with 6 elements.

719 is the number of rooted trees with 10 vertices.

720 = 6!

721 is the smallest number which can be written as the difference of two cubes in 2 ways.

724 is the number of diffe! ! rent arrangements of 10 non-attacking queens on an 10×10 chessboard.

726 is a pentagonal pyramidal number.

727 has the property that its square is the concatenation of two consecutive numbers.

728 is the smallest number n where n and n+1 are both products of 5 or more primes.

729 = 36.

730 is the number of connected bipartite graphs with 9 vertices.

731 is the number of planar partitions of 14.

732 = 17 + 26 + 35 + 44 + 53 + 62 + 71.

733 = 7 + 3! + (3!)!

734 is the smallest number that can be written as the sum of 3 distinct non-zero squares in 10 ways.

735 is the smallest number that is the concatenation of its distinct prime factors.

736 is a strong Friedman number.

739 has a base 2 representation that begins with its base 9 representation.

742 is the smallest number that is one more than triple its reverse.

743 is the number of independent sets of the graph of the 4-dimensional hypercube.

746 = 17 + 24 + 36.

750 is the Stirling number of the second kind S(10,8).

752 is the number of conjugacy classes in the automorphism group of the 11 dimensional hypercube.

757 is the smallest number whose reciprocal has a period of 27.

760 is the number of partitions of 37 into distinct parts.

762 is the first decimal digit of where a digit occurs four times in a row.

764 is the number of 8×8 symmetric permutation matrices.

765 is a Kaprekar constant in base 2.

767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution.

773 is the smallest odd number n so that n+2k is composite for all k<n.

777 is a repdigit in bases 6 and 10.

780 = (5+7)(5+8)(5+0).

781 = 11111 in base 5.

784 is the sum of the first 7 cubes.

786 is the largest known n for which 2nCn is not divisible by the square of an odd prime.

787 is a palindromic prime.

788 is the smallest of 6 consecutive numbers divisible by 6 consecutive primes.

791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12.

792 is the number of partitions of 21.

793 is one less than twice its reverse.

794 is the sum of the first 3 6th powers.

797 is the number of functional graphs on 9 vertices.

800 = 2222 in base 7.

802 is the number of isomers of C13H28.

810 is divisible by its reverse.

816 = 18C3.

819 is the smallest number so that it and its successor are both the product of 2 primes and the square of a prime.

820 = 1111 in base 9.

822 is the number of planar graphs with 7 vertices.

835 is the 9th Motzkin number.

836 is a non-palindrome with a palindromic square.

839 has a base 5 representation that begins with its base 9 representation.

840 is the smallest number divisble by 1 through 8.

841 is a square that is also the sum of 2 consecutive squares.

842 is a value of n for which n!! – 1 is prime.

843 is the 14th Lucas number.

844 is the smallest number so that it and the next 4 numbers are all squareful.

846 has the property that its square is the concatenation of two consecutive numbers.

853 is the number of connected graphs with 7 vertices.

854 has the property that it and its square together use the digits 1-9 once.

855 is the smallest number which is the sum of 5 consecutive squares or 2 consecutive cubes.

858 is the smallest palindrome with 4 different prime factors.

864 is the number of partitions of 38 into distinct parts.

866 is the number of sided 10-iamonds.

870 is the sum of its digits and the cube of its digits.

872 is a value of n for which n!+1 is prime.

873 = 1! + 2! + 3! + 4! + 5! + 6!

877 is the 7th Bell number.

880 is the number of 4 x 4 magic squares.

888 has a cube whose digits each occur 3 times.

889 is a Kaprekar constant in base 2.

891 is an octahedral number.

894 has a base 5 representation that begins with its base 9 representation.

895 is a Woodall number.

896 is not the sum of 4 non-zero squares.

899 is the product of twin primes.

900 has a base 5 representation that begins with its base 9 representation.

901 is the sum of the digits of the first 100 positive integers.

906 is the number of perfect graphs with 7 vertices.

907 is the largest n so that Q(n) has class number 3.

912 has exactly the same digits in 3 different bases.

913 has exactly the same digits in 3 different bases.

914 is the number of binary rooted trees with 15 vertices.

919 is the smallest number which is not the difference between palindromes.

922 = 1234 in base 9.

924 is the 6th central binomial coefficient.

925 is the number of partitions of 37 in which no part occurs only once.

927 is the 13th tribonacci number.

929 is a palindromic prime.

936 is a pentagonal pyramidal number.

941 is the smallest number which is the reverse of the sum of its proper substrings.

945 is the smallest odd abundant number.

946 is a hexagonal pyramidal number.

951 is the number of functions from 8 unlabeled points to themselves.

952 = 93 + 53 + 23 + (9)(5)(2).

957 is a value of n for which sigma(n)=sigma(n+1).

960 is the sum of its digits and the cube of its digits.

! ! 961 is a square whose digits can be rotated to give another square.

966 is the Stirling number of the second kind S(8,3).

969 is a tetrahedral palindrome.

976 has a square formed by inserting a block of digits inside itself.

979 is the sum of the first 5 4th powers.

981 is the smallest number that has 5 different partitions into 3 parts with the same product.

982 is the number of partitions of 39 into distinct parts.

985 = 4321 in base 6.

986 = 19 + 28 + 36.

987 is the 16th Fibonacci number.

990 is a triangular number that is the product of 3 consecutive integers.

991 is a permutable prime.

992 is the number of differential structures on the 11-dimensional hypersphere.

993 is the smallest number with the property that its first 15 multiples contain the digit 9.

994 is the smallest number with the property that its first 18 multiples contain the digit 9.

995 has a ! ! square formed by inserting a block of digits inside itself.

996 has a square formed by inserting a block of digits inside itself.

997 is the smallest number with the property that its first 37 multiples contain the digit 9.

998 is the smallest number with the property that its first 55 multiples contain the digit 9.

999 is a Kaprekar number.

1000 = 103.

1001 is the smallest palindromic product of 3 consecutive primes.

1002 is the number of partitions of 22.

1003 has a base 2 representation that ends with its base 3 representation.

1005 is the smallest number whose English name contains all five vowels exactly once.

1006 has a cube that is a concatenation of other cubes.

1009 is the smallest number which is the sum of 3 distinct positive cubes in 2 ways.

1011 has a square that is formed by inserting three 2’s into it.

1012 has a square that is formed by inserting three 4’s into it.

1016 is a stella octangula number.

1019 is a value of n for which one more than the product o! ! f the first n primes is prime.

1021 is a value of n for which one more than the product of the first n primes is prime.

1022 is a Friedman number.

1023 is the smallest number with 4 different digits.

1024 is the smallest number with 11 divisors.

1025 is the smallest number that can be written as the sum of a square and a cube in 4 ways.

1029 is the smallest order for which there are 19 groups.

1031 is the length of the largest repunit that is known to be prime.

1033 = 81 + 80 + 83 + 83.

1035 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

1036 = 4444 in base 6.

1044 is the number of graphs with 7 vertices.

1050 is the Stirling number of the second kind S(8,5).

1052 has the property that placing the last digit first gives 1 more than twice it.

1056 is the area of the smallest non-square rectangle that can be tiled with integer-sided squares.

1067 has exactly the same digits in 3 different bases.

1078 is the number of lattices on 9 unlabeled nodes.

1079 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 15.

1080 is the smallest number with 18 divisors.

1084 is the smallest number whose English name contains all five vowels in order.

1089 is one ninth of its reverse.

1092 is the order of a non-cyclic simple group.

1093 is the smallest Wieferich prime.

1098 = 11 + 0 + 999 + 88.

1099 = 1 + 0 + 999 + 99.

1100 has a base 3 representation that ends with 1100.

1101 has a base 2 representation that ends with 1101.

1104 is a Keith number.

1105 is a rhombic dodecahedral number.

1106 is a truncated tetrahedral number.

1111 is a repdigit.

1112 has a base 3 representation that begins with 1112.

1113 is the number of partitions of 40 into distinct parts.

1116 is the number of polyaboloes with 8 half squares.

1122 = 33C1 + 33C1 + 33C2 + 33C2.

1123 has digits which start the Fibonacci sequence.

1124 is a number whose product of digits is equal to its sum of digits.

1139 has the property that placing the last digit first gives 1 more than 8 times it.

1140 is the smallest number whose divisors contain every digit at least three times.

1141 is the smallest number whose 6th power can be written as the sum of 7 6th powers.

1142 is a number whose product of digits is equal to its sum of digits.

1148 is the number of ways to fold a strip of 9 stamps.

1152 is a highly totient number.

1153 is the smallest number with the property that its first 3 multiples contain the digit 3.

1155 is the product of 4 consecutive primes.

1156 is a square whose digits are non-decreasing.

1161 is the number of degree 14 irreducible polynomials over GF(2).

1165 is the number of conjugacy classes in the automorphism group of the 12 dimensional hypercube.

1166 is a heptagonal pyramidal number.

1167 is the smallest number whose 8th power can be written as the sum of 9 8th powers.

1170 = 2222 in base 8.

1171 has a 4th power containing only 4 different digits.

1183 is the smallest number with the property that its first 4 multiples contain the digit 3.

1184 is an amicable number.

1185 = 11 + 1111 + 8 + 55.

1186 is the number of 11-iamonds.

! ! 1187 = 111 + 111 + 888 + 77.

1189 is the square root of a triangular number.

1193 and its reverse are prime, even if we append or prepend a 3 or 9.

1197 is the smallest number that contains as substrings the maximal prime powers that div! ! ide it.

1200 = 3333 in base 7.

1201 has a square that is formed by inserting three 4’s into it.

1206 is a Friedman number.

1207 is the product of two primes which are reverses of each other.

! ! 1210 is an amicable number.

1214 is a number whose product of digits is equal to its sum of digits.

1215 is the smallest number n where n and n+1 are both products of 6 or more primes.

1222 is a hexagonal pyramidal number.

1224 is the smallest number that can be written as the sum of 4 cubes in 3 ways.

1225 is a hexagonal square triangular number.

1229 is the number of primes less than 10000.

1230 has the property that 17 + 27 + 37 + 07 equals 1230 written in base 8.

1231 has the property that 17 + 27 + 37 + 17 equals 1230 written in base 8.

1233 = 122 + 332.

1234 is the first four positive digits.

1241 is a centered cube number.

1243 is the number of essentially different ways to dissect a 18-gon into 8 quadrilaterals.

1246 is the number of partitions of 38 in which no part occurs only once.

1248 is the smallest number with the property that its first 6 multiples contain the digit 4.

1249 is the number! ! of simplicial polyhedra with 11 vertices.

1255 is a Friedman number.

1260 is the smallest number with 36 divisors.

1275 has a square that is formed by 3 squares that overlap by 1 digit.

1276 = 1111 + 22 + 77 + 66.

1278 = 1111 + 2 + 77 + 88.

1279 is the exponent of a Mersenne prime.

1285 is the number of 9-ominoes.

1287 = 13C5.

1294 is the number of 4 dimensional polytopes with 8 vertices.

1295 = 5555 in base 6.

1296 is a Friedman number.

1297 has a base 2 and base 3 representation that ends with its base 6 representation.

1298 has a base 3 representation that ends with its base 6 representation.

1300 is the sum of the first 4 5th powers.

1301 is the number of trees with 13 vertices.

1306 = 11 + 32 + 03 + 64.

1310 is the smallest number so that it and its neighbors ar! ! e products of three primes.

1320 = 12P3.

1330 = 21C3.

1331 is a cube containing only odd digits.

1332 has a base 2 representation that begins and ends with its base 6 representation.

1333 has a base 2 representation that ends with its base 6 representation.

1334 is a value of n for which sigma(n)=sigma(n+1).

1364 is the 15th Lucas number.

1365 = 15C4.

1366 = 1 + 33 + 666 + 666.

1368 is the number of ways to fold a 3×3 rectangle of stamps.

1369 is a square whose digits are non-decreasing.

1370 = 12 + 372 + 02.

1371 = 12 + 372 + 12.

1376 is the smallest number with the property that it and its neighbors are not cubefree.

1385 is the 8th Euler number.

1386 = 1 + 34 + 8 + 64.

1395 is a vampire number.

1405 is the sum of consecutive squares in 2 ways.

1412 is a number whose product of digits is equal to its sum of digits.

1419 is a Zeisel number.

1421 is a number whose product of digits is equal to its sum of digits.

1426 is the number of partitions of 42 into distinct parts.

1429 is the smallest number whose square has the first 3 digits the same as the next 3 digits.

1430 is the 8th Catalan number.

1435 is a vampire number.

1444 is a square whose digits are non-decreasing.

1448 is the number of 8-hexes.

1449 is a stella octangula number.

1453 = 1111 + 4 + 5 + 333.

1454 = 11 + 444 + 555 + 444.

1455 is the number of subgroups of the symmetric group on 6 symbols.

1458 is the maximum determinant of a 11 x 11 matrix of 0’s and 1’s.

1459 = 11 + 444 + 5 + 999.

1465 has a square that is formed by inserting three 2’s into it.

1467 has the property that e1467 is within 10-8 of an integer.

1469 is an octahedral number.

1470 is a pentagonal pyramidal number.

1476 is the number of graphs with 9 edges.

1477 is a value of n for which n!+1 is prime.

1490 is the 14th tetranacci number.

1494 is the sum of its proper divisors that contain the digit 4.

1500 = (5+1)(5+5)(5+0)(5+0).

1503 is a Friedman number.

1506 is the sum of its proper divisors that contain the digit 5.

1508 is a heptagonal pyramidal number.

1514 is a number whose square and cube use different digits.

1518 is the sum of its proper divisors that contain the digit 5.

1521 is the smallest number that can be writte! ! n as the sum of 4 distinct cubes in 3 ways.

1530 is a vampire number.

1531 appears inside its 4th power.

1533 is a Kaprekar constant in base 2.

1534 = 4321 in base 7.

1536 is not the sum of 4 non-zero squares.

1537 has its largest proper divisor as a substring.

1540 is a tetrahedal triangular number.

1543 = 1111 + 55 + 44 + 333.

1547 is a hexagonal pyramidal number.

1555 is the largest n so that Q(n) has class number 4.

1557 has a square where the first 6 digits alternate.

1562 = 22222 in base 5.

1563 is the smallest number with the property that its first 4 multiples contain the digit 6.

1573 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

1575 is the number of partitions of 24.

1581 is the smallest number whose 8th power contains exactly the same digits as another 8th power.

1584 has a base 3 representation that ends with its base 6 representation.

1585 has a base 3 representation that ends with its base 6 representation.

1586 has a base 3 representation that ends with its base 6 representation.

1595 is the smallest quasi-Carmichael number in base 2.

1597 is the 17th Fibonacci number.

1600 = 4444 in base 7.

1606 is the number of strongly connected digraphs with 4 vertices.

1610 is the number of partitions of 43 into distinct parts.

1624 is the Stirling number of the first kind s(7,3).

1632 is the smallest number with the property that its first 5 multiples contain the digit 6.

1633 is a number whose square and cube use different digits.

1634 = 14 + 64 + 34 + 44.

1636 appears inside its 4th power.

1638 is a harmonic divisor number.

1639 is the number of binary rooted trees with 16 vertices.

1640 = 2222 in base 9.

1650 is the number of connected partial orders on 7 unlabeled elements.

1663 is the number of partitions of 41 in which no part occurs only once.

1666 is the sum of the Roman numerals.

1676 = 11 + 62 + 73 + 64.

1680 is the smallest number with 40 divisors.

1681 is a square and each of its two 2-digit parts is square.

1688 is a truncated tetrahedral number.

1689 is the smallest composite number all of whose divisors (except 1) contain the digit 9.

1692 has a square with the first 3 digits the same as the next 3 digits.

1695 is a rhombic dodecahedral number.

1701 is the Stirling number of the ! ! second kind S(8,4).

1705 is the smallest quasi-Carmichael number in base 4.

1710 is the smallest non-palindrome where it and its reverse are divisible by 19.

1715 = (1) (7)3 (1) (5).

1716 = 13C6.

1722 is a Giuga number.

1728 = 123.

1729 is the smallest number which can be written as the sum of 2 cubes in 2 ways.

1730 is the sum of consecutive squares in 2 ways.

1734 is the sum of its proper divisors that contain the digit 8.

1739 has a base 5 representation that begins with its base 9 representation.

1740 has a base 5 representation that begins with its base 9 representation.

1755 = 3333 in base 8.

1763 is the product of twin primes.

1764 is the Stirling number of the first kind s(7,2).

1770 is the number of conjugacy classes in the automorphism group of the 13 dimensional hypercube.

1771 is a tetrahedral palindrome.

1782 is the smallest number n that is 3 times the sum of all the 2-digit numbers that can be made using the digits of n.

1785 is a Kaprekar constant in base 2.

1787 is the number of different arrangements (up to rotation and reflection) of 12 non-attacking queens on a 12×12 chessboard.

1789! ! is the smallest number with the property that its first 4 multiples contain the digit 7.

1792 is a Friedman number.

1794 has a base 5 representation that begins with its base 9 representation.

1795 has a base 5 representation that begins with its base 9 representation.

1800 is a pentagonal pyramidal number.

1816 is the number of partitions of 44 into distinct parts.

1818 evenly divides the sum of its rotations.

1820 = 16C4.

1822 has a cube that contains only even digits.

1823 has a square with the first 3 digits the same as the next 3 digits.

1824 has a cube that contains only even digits.

1827 is a vampire number.

1828 is the 11th meandric number.

1834 is an octahedral number.

1842 is the number of rooted trees with 11 vertices.

1849 is the smallest composite number all of whose divisors (except 1) contain the digit 4.

1854 is the number of derangements of 7 items.

1858 is the number of isomers of C14H30.

1865 = 12345 in base 6.

1873 is a value of n for which one less than the product of the first n primes is prime.

1875 is the smallest! ! order for which there are 21 groups.

1885 is a Zeisel number.

1890 is the smallest number whose divisors contain every digit at least four times.

1895 is a value of n for which n, 2n, 3n, 4n, 5n, and 6n all use the same number of digits in Roman numerals.

1900 is the largest palindrome in Roman numerals.

1902 has a cube that contains only even digits.

1905 is a Kaprekar constant in base 2.

1908 is the number of self-dual planar graphs with 22 edges.

1911 is a heptagonal pyramidal number.

1913 is prime and contains the same digits as the next prime.

1915 is the number of semigroups of order 5.

1920 is the smallest number that contains more different digits than its cube.

1925 is a hexagonal pyramidal number.

1944 is a member of the Fibonacci-like multiplication series starting with 2 and 3.

1947 is the number of planar partitions of 16.

1953 is a Kaprekar constant in base 2.

1958 is the number of partitions of 25.

1960 is the Stirling number of the first kind s(8,5).

1964 is the number of legal knight moves in chess.

1969! ! is the only known counterexample to a conjecture about modular Ackermann functions.

1980 is the number of ways to fold a 2×4 rectangle of stamps.

1990 is a stella octangula number.

1998 is the largest number that is the sum of its digits and the cube of its digits.

2000 = 5555 in base 7.

2001 has a square with the first 3 digits the same as the next 3 digits.

2002 = 14C5.

2004 has a square with the last 3 digits the same as the 3 digits before that.

2008 is a Kaprekar constant in base 3.

2020 is a curious number.

2024 = 24C3.

2025 is a square that remains square if all its digits are incremented.

2030 ! ! is the smallest number that can be written as a sum of 3 or 4 consecutive squares.

2038 is the number of Eulerian graphs with 9 vertices.

2041 is a 12-hyperperfect number.

2045 is the number of unlabeled partially ordered sets of 7 elements.

2047 is the smallest composite Mersenne number with prime exponent.

2048 is the smallest 11th power (besides 1).

2053 is a value of n for which one less than the product of the first n primes is prime.

2073 is a Genocchi number.

2082 is the sum of its proper divisors that contain the digit 4.

2100 is divisible by its reverse.

2114 is a number whose product of digits is equal to its sum of digits.

2116 has a base 10 representation which is the reverse of its base 7 representation.

2132 is the maximum number of 11th powers needed to sum to any number.

2133 is a 2-hyperperfect number.

2141 is a number whose product of digits is equal to its sum of digits.

2143 is the number of commutative semigroups of order 6.

2147 has a square with the last 3 digits the same as the 3 digits before that.

2164 is the smallest number whose 7th power starts with 5 identical digits.

2176 is the number of prime knots with 12 crossings.

2178 is the only number known which when multiplied by its reverse yields a fourth power.

2182 is the number of degree 15 irreducible polynomials over GF(2).

2184 = 14P3.

2185 is the number of digits of 555.

2186 = 2222222 in ! ! base 3.

2187 is a strong Friedman number.

2188 is the 10th Motzkin number.

2194 is the number of partitions of 42 in which no part occurs only once.

2197 = 133.

2201 is the only non-palindrome known to have a palindromic cube.

2202 is the number of partitions of 43 in which no part occurs only once.

2203 is the exponent of a Mersenne prime.

2207 is the 16th Lucas number.

2208 is a Keith number.

2210 = 47C2 + 47C2 + 47C1 + 47C0.

2213 = 23 + 23 + 133.

2217 has a base 2 representation that begins with its base 3 representation.

2222 is the smallest number divisible by a 1-digit prime, a 2-digit prime, and a 3-digit prime.

2223 is a Kaprekar number.

2244 is a number whose square and cube use different digits.

2255 is an octahedral number.

2257 = 4321 in base 8.

2261 = 2222 + 22 + 6 + 11.

2263 = 2222 + 2 + 6 + 33.

2272 has a cube that is a concatenation of other cubes.

2273 is the number of functional graphs on 10 vertices.

2274 is the sum of its proper divisors that contain the digit 7.

2275 is the sum of the first 6 4th powers.

2281 is the exponent of a Mersenne prime.

2285 is a non-palindrome with a palindromic square.

2295 is the number of self-dual binary codes of length 12.

2300 = 25C3.

2303 is a number whose square and cube use different digits.

2304 is the number of edges in a 9 dimensional hypercube.

2305 has a base 6 representation that ends with its base 8 representation.

2306! ! has a base 6 representation that ends with its base 8 representation.

2307 has a base 6 representation that ends with its base 8 representation.

2308 has a base 6 representation that ends with its base 8 representation.

2309 has a base 6 representation that ends with its base 8 representation.

2310 is the product of the first 5 primes.

2312 has a square with the first 3 digits the same as the next 3 digits.

2318 is the number of connected planar graphs with 10 edges.

2322 is the number of connected graphs with 10 edges.

2328 is the number of groups of order 128.

2331 is a centered cube number.

2336 is the number of sided 11-iamonds.

2340 = 4444 in base 8.

2343 = 33333 in base 5.

2349 is a Friedman number.

2354 = 2222 + 33 + 55 + 44.

2357 is the concatenation of the first 4 primes.

2359 = 2222 + 33 + 5 + 99.

2360 is a hexagonal pyramidal number.

2377 is a value of n for which one less than the product of the first n primes is prime.

2380 = 17C4.

2385 is the smallest number whose 7th power contains exactly the same digits as another 7th power.

2388 is the number of 3-connected graphs with 8 vertices.

2400 = 6666 in base 7.

2401 is the 4th power of the sum of its digits.

2402 has a base 2 representation that begins with its base 7 representation.

2408 is a number whose product of digits is equal to its sum of digits.

2411 is a number whose product of digits is equal to its sum of digits.

2417 has a base 3 representation that begins with its base 7 representation.

2427 = 21 + 42 + 23 + 74.

2431 is the product of 3 consecutive primes.

2434 is the number of legal king moves in chess.

2436 is the number of partitions of 26.

2437 is the smallest number which is not prime when preceded or followed by any digit 1-9.

2445 is a truncated tetrahedral number.

2448 is the order of a non-cyclic simple group.

2450 has a base 3 representation that begins with its base 7 representation.

2460 = 3333 in base 9.

2465 is a Carmichael number.

2467 has a square with the first 3 digits the same as the next 3 digits.

2499 is the number of connected planar Eulerian graphs with 10 vertices.

2500 is a Friedman number.

2501 is a Friedman number.

2502 is a strong Friedman number.

2503 is a Friedman number.

2504 is a Friedman number.

2505 is a Friedman number.

2506 is a Friedman number.

2507 is a Friedman number.

2508 is a Friedman number.

2509 is a Friedman number.

2511 is the smallest number so that it and its successor are both the product of a prime and the 4th power of a prime.

2519 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 12.

2520 is the smallest number divisible by 1 through 10.

2532 = 2222 + 55 + 33 + 222.

2538 has a square with 5/7 of the digits are the same.

2550 is a Kaprekar constant in base 4.

2571 is the smallest number with the property that its first 7 multiples contain the digit 1.

2576 has exactly the same digits in 3 different bases.

2580 is a Keith number.

2584 is the 18th Fibonacci number .

2590 is the number of partitions of 47 into distinct parts.

2592 is a strong Friedman number.

2592 has a base 3 representation that ends with its base 6 representation.

2593 has a base 3 representation that ends with its base 6 representation.

2594 has a base 3 representation that ends with it! ! s base 6 representation.

2600 = 26C3.

2601 is a pentagonal pyramidal number.

2606 is the number of polyhedra with 9 vertices.

2615 is the number of functions from 9 unlabeled points to themselves.

2620 is an amicable number.

2621 = 2222 + 66 + 222 + 111.

2623 = 2222 + 66 + 2 + 333.

2629 is the smallest number whose reciprocal has period 14.

2636 is a non-palindrome with a palindromic square.

2646 is the Stirling number of the second kind S(9,6).

2651 is a stella octangula number.

2657 is a value of n for which one more than the product of the first n primes is prime.

2662 is a palindrome and the 2662nd triangular number is a palindrome.

2665 is the number of conjugacy classes in the automorphism group of the 14 dimensional hypercube.

2673 is the smallest number that can be written as the sum of 3 4th powers in 2 ways.

2680 is the number of different arrangements of 11 non-attacking queens on an 11×11 chessboard.

2683 is the largest n so that Q(n) has class number 5.

2685 is a value of n for which sigma(n)=sigma(n+1).

2694 is the number of ways 22 people around a round table can shake hands in a non-crossing way, up to rotation.

2697 and its product with 5 contain every digit from 1-9 exactly once.

2700 is the product of the first 5 triangular numbers.

2701 is the smallest number n which divides the average of the nth prime and the primes surrounding it.

2728 is a Kaprekar number.

2729 has a square with the first 3 digits the same as the next 3 digits.

2730 = 15P3.

2736 is an octahedral number.

2737 is a strong Friedman number.

2744 = 143.

2745 divides the sum of the primes less than it.

2758 has the property that placing the last digit first gives 1 more than triple it.

2780 = 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81.

2801 = 11111 in base 7.

2802 is the sum of its proper divisors that contain the digit 4.

2805 is the smallest order of a cyclotomic polynomial whose factorization contains 6 as a coefficient.

2821 is a Carmichael number.

2842 is the smallest number with the property that its first 4 multiples contain the digit 8.

2856 is a hexagonal pyramidal number.

2857 is the number of partitions of 44 in which no part occurs only once.

2858 has a square with the first 3 digits the same as the next 3 digits.

2868 has a 4th power containing only 4 different digits.

2872 is the 15th tetranacci number.

2880 is the smallest number that can be written in the form (a2-1)(b2-1) in 3 ways.

2881 has a base 3 representation that ends with its base 6 representation.

2882 has a base 3 representation that ends with its base 6 representation.

2890 is the smallest number in base 9 whose square contains the same digits in the same proportion.

2893 is the number of planar 2-connected graphs with 8 vertices.

2910 is the number of partitions of 48 into distinct parts.

2916 is a Friedman number.

2920 is a heptagonal pyramidal number.

2922 is the sum of its proper divisors that contain the digit 4.

2924 is an amicable number.

2925 = 27C3.

2928 is the number of partitions of 45 in which no part occurs only once.

2931 is the reverse of the sum of its proper substrings.

2938 is the number of binary rooted trees with 17 vertices.

2947 is the smallest number whose 5th power starts with 4 identical digits.

2955 has a 5th power whose digits all occur twice.

2970 is a harmonic divisor number.

2974 is a value of n for which sigma(n)=sigma(n+1).

2996 = 2222 + 99 + 9 + 666.

2997 = 222 + 999 + 999 + 777.

2999 = 2 + 999 + 999 + 999.

3003 is the only number known to appear 8 times in Pascal’s triangle.

3006 has a square with the last 3 digits the same as the 3 digits before that.

3010 is the number of partitions of 27.

3012 is the sum of its proper divisors that contain the digit 5.

3015 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

3024 = 9P4.

3025 is the sum of the first 10 cubes.

3036 is the sum of its proper divisors that contain the digit 5.

3059 is a centered cube number.

3060 = 18C4.

3068 is the number of 10-ominoes that tile the plane.

3069 is a Kaprekar constant in base 2.

3078 is a pentagonal pyramidal number.

3097 is the largest known number n with the property that in every base, there exists a number that is n times the sum of its digits.

3103 = 22C3 + 22C1 + 22C0 + 22C3.

3106 is both the sum of the digits of the 16th and the 17th Mersenne prime.

3110 = 22222 in base 6.

3114 has a square containing only 2 digits.

3120 is the product of the first 6 Fibonacci numbers.

3124 = 44444 in base 5.

3125 is a strong Friedman number.

3126 is a Sierpinski Number of the First Kind .

3135 is the smallest order of a cyclotomic polynomial whose factorization contains 7 as a coefficient.

3136 is a square that remains square if all its digits are decremented.

3137 is the number of planar partitions of 17.

3148 has a square with the first 3 digits the same as the next 3 digits.

3150 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

3156 is the sum of its proper divisors that contain the digit 5.

3159 is the number of trees with 14 vertices.

3160 is the largest known n for which 2n!/(n!)2 does not contain a prime factor less than 12.

3168 has a square whose reverse is also a square.

3174 is the sum of its proper divisors that contain the digit 5.

3178 = 4321 in base 9.

3180 has a base 3 representation that ends with its base 5 representation.

3181 has a base 3 representation that ends with its base 5 representation.

3182 has a base 3 representation that ends with its base 5 representation.

3187 and its product with 8 contain every digit from 1-9 exactly once.

3191 is the smallest number whose reciprocal has period 29.

3210 is the smallest 4-digit number with decreasing digits.

3212 = 37 + 29 + 17 + 29.

3216 is the smallest number with the property that its first 6 multiples contain the digit 6.

3217 is the exponent of a Mersenne prime.

3229 is a value of n for which one more than the product of the first n primes is prime.

3242 has a square with the first 3 digits the same as the next 3 digits.

3248 is the number of legal b! ! ishop moves in chess.

3249 is the smallest square that is comprised of two squares that overlap in one digit.

3254 = 33 + 2222 + 555 + 444.

3259 = 33 + 2222 + 5 + 999.

3264 is the number of partitions of 49 into distinct parts.

3267 = 12345 in base 7.

3276 = 28C3.

3280 = 11111111 in base 3.

3281 is the sum of consecutive squares in 2 ways.

3282 is the sum of its proper divisors that contain the digit 4.

3301 is a value of n for which the nth Fibonacci number begins with the digits in n.

3313 is the smallest prime number where every digit d occurs d times.

3318 has exactly the same digits in 3 different bases.

3320 has! ! a base 4 representation that ends with 3320.

3321 has a base 4 representation that ends with 3321.

3322 has a base 4 representation that ends with 3322.

3323 has a base 4 representation that ends with 3323.

3333 is a repdigit.

3334 is the number of 12-iamonds.

3340 = 3333 + 3 + 4 + 0.

3341 = 3333 + 3 + 4 + 1.

3342 = 3333 + 3 + 4 + 2.

3343 = 3333 + 3 + 4 + 3.

3344 = 3333 + 3 + 4 + 4.

3345 = 3333 + 3 + 4 + 5.

3346 = 3333 + 3 + 4 + 6.

3347 = 3333 + 3 + 4 + 7.

3348 = 3333 + 3 + 4 + 8.

3349 = 3333 + 3 + 4 + 9.

3360 = 16P3.

3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways.

3368 is the number of ways that 8 non-attacking bishops can be placed on a 5×5 chessboard.

3369 is a Kaprekar constant in base 4.

3375 is a Friedman number.

3378 is a Friedman number.

3379 is a number whose square and cube use different digits.

3400 is a truncated tetrahedral number.

3413 = 11 + 22 + 33 + 44 + 55.

3417 is a hexagonal pyramidal number.

3420 is the order of a non-cyclic simple group.

3432 is the 7th central binomia! ! l coefficient.

3435 = 33 + 44 + 33 + 55.

3439 is a rhombic dodecahedral number.

3444 is a stella octangula number.

3465 is the smallest number with the property that its first 5 multiples contain the digi! ! t 3.

3468 = 682 – 342.

3476 is a value of n for which n!! – 1 is prime.

3486 has a square that is formed by 3 squares that overlap by 1 digit.

3489 is the smallest number whose square has the first 3 digits the same as the last 3 digits.

3492 is the number of labeled semigroups of order 4.

3501 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

3510 = 6666 in base 8.

3511 is the largest known Wieferich prime.

3521 = 3333 + 55 + 22 + 111.

3522 is the sum of its proper divisors that contain the digit 7.

3527 is the number of ways to fold a strip of 10 stamps.

3536 is a heptagonal pyramidal number.

3541 is the smallest number whose reciprocal has period 20.

3543 has a cube containing only 3 different digits.

3571 is the 17th Lucas number.

3577 is a Kaprekar constant in base 2.

3584 is not the sum of 4 non-zero squares.

3599 is the product of twin primes.

3600 is a value of n for which n, 2n, 3n, 4n, 5n, 6n, and 7n all use the same number of digits in Roman numerals.

3610 is a pentagonal pyramidal number.

3624 is the smallest number n where n through n+3 are all products of 4 or more primes.

3630 appears inside its 4th power.

3635 has a square with the first 3 digits the same as the next 3 digits.

3645 is the maximum determinant of a 12 x 12 matrix of 0’s and 1’s.

3654 = 29C3.

3655 is the sum of consecutive squares in 2 ways.

3658 is the number of partitions of 50 into distinct parts.

3678 has a square comprised of the digits 1-8.

3684 is a Keith number.

3685 is a strong Friedman number.

3697 is the smallest number in base 6 whose square contains the same digits in the same proportion.

3698 has a square comprised of the digits 0-7.

3718 is the number of partitions of 28.

3721 is the number of partitions of 46 in which no part occurs only once.

3740 is the sum of consecutive squares in 2 ways.

3743 is the number of polyaboloes with 9 half squares.

3745 has a square with the last 3 digits the same as the 3 digits before that.

3747 is the smallest number whose 9th power contains exactly the same digits as another 9th power.

3763 is the largest n so that Q(n) has class number 6.

3784 has a factorization using the same digits as itself.

3786 = 34 + 74 + 8 + 64.

3792 occurs in the middle of its square.

3813 is the number of partitions of 47 in which no part occurs only once.

3825 is a Kaprekar constant in base 2.

3836 is the maximum number of inversions in a permutation of length 7.

3840 = 10!!

3849 has a square with the first 3 digits the same as the next 3 digits.

3861 is the smallest number whose 4th power starts with 5 identical digits.

3864 is a strong Friedman number.

3873 is a Kaprekar constant in base 4.

3876 = 19C4.

3882 is the sum of its proper divisors that contain the digit 4.

3894 is an octahedral number.

3900 has a base 2 representation that is two copies of its base 5 representation concatenated.

3901 has a base 2 representation that ends with its base 5 representation.

3906 = 111111 in base 5.

3911 and its reverse are prime, even if we append or prepend a 3 or 9.

3920 = (5+3)(5+9)(5+2)(5+0).

3925 is a centered cube number.

3926 is the 12th meandric number.

3937 is a Kaprekar constant in base 2.

3956 is the number of conjugacy classes in the automorphism group of the 15 dime! ! nsional hypercube.

3967 is the smallest number whose 12th power contains exactly the same digits as another 12th power.

3969 is a Kaprekar constant in base 2.

3972 is a strong Friedman number.

3977 has its largest proper divisor as a substring.

3985 = 3333 + 9 + 88 + 555.

4000 has a cube that contains only even digits.

4002 has a square with the first 3 digits the same as the next 3 digits.

4006 = 14C4 + 14C0 + 14C0 + 14C6.

4008 has a square with the last 3 digits the same as the 3 digits before that.

4030 is an abundant number that is not the sum of some subset of its divisors.

4032 is the number of connected bipartite graphs with 10 vertices.

4047 is a hexagonal pyramidal number.

4048 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4051 is the number of partitions of 6 items into ordered lists.

4060 = 30C3.

4062 is the smallest number with the property that its first 8 multiples contain the digit 2.

4080 = 17P3.

4093 is a value of n for which one less than the product of the first n primes is prime.

4095 = 111111111111 in base 2.

4096 is the smallest number with 13 divisors.

4097 is the smallest number (besides 2) that can be written as the sum of two cubes or the sum of two 4th powers.

4099 has a square with the last 3 digits the same as the 3 digits before that.

4100 = 5555 in base 9.

4104 can be written as the sum of 2 cubes in 2 ways.

4106 is a Friedman number.

4112 is a number whose product of digits is equal to its sum of digits.

4121 is a number whose p! ! roduct of digits is equal to its sum of digits.

4128 is the smallest number with the property that its first 10 multiples contain the digit 2.

4140 is the 8th Bell number.

4150 = 45 + 15 + 55 + 05.

4151 = 45 + 15 + 55 + 15.

4152 = 45 + 15 + 55 + 2.

4153 = 45 + 15 + 55 + 3.

4154 = 45 + 15 + 55 + 4.

4155 = 45 + 15 + 55 + 5.

4156 = 45 + 15! ! + 55 + 6.

4157 = 45 + 15 + 55 + 7.

4158 = 45 + 15 + 55 + 8.

4159 = 45 + 15 + 55 + 9.

4160 = 43 + 163 + 03.

4161 = 43 + 163 + 13.

4167 is a Friedman number.

4175 has a square comprised of the digits 0-7.

4181 is the first composite number in the Fibonacci sequence with a prime index.

4186 is a hexagonal, 13-gonal, triangular number.

4187 is the smallest Rabin-Miller pseudoprime with an odd reciprocal period.

4199 is the product of 3 consecutive primes.

4200 is divisible by its reverse.

4207 is the number of cubic graphs with 16 vertices.

4211 is a number whose product of digits is equal to its sum of digits.

4223 is the maximum number of 12th powers needed to sum to any number.

4224 is a palindrome that is one less than a square.

4231 is the number of labeled partially ordered sets with 5 elements.

4233 is a heptagonal pyramidal number.

4243 = 444 + 22 + 444 + 3333.

4253 is the exponent of a Mersenne prime.

4293 has exactly the same digits in 3 different bases.

4297 is a value of n for which one less than the product of the first n primes is prime.

4305 has exactly the same digits in 3 different bases.

4310 has exactly the same digits in 3 different bases.

4312 is the smallest number whose 10th power starts with 7 identical digits.

4320 = (6+4)(6+3)(6+2)(6+0).

4321 is the first four digits in decreasing order.

4332 = 444 + 3333 + 333 + 222.

4335 = 444 + 3333 + 3 + 555.

4336 = 4 + 3333 + 333 + 666.

4339 = 4 + 3333 + 3 + 999.

4342 appears inside its 4th power.

4347 is a heptagonal pentagonal number.

4352 has a cube that contains only even digits.

4356 is two thirds of its reversal.

4357 is the smallest number with the property that its first 5 multiples contain the digit 7.

4364 is a value of n for which sigma(n)=sigma(n+1).

4368 = 16C5.

4381 is a stella octangula number.

4396 = (157)(28) and each digit is contained in the equation exactly once.

4409 is prime, but changing any digit makes it composite.

4423 is the exponent of a Mersenne prime.

4425 is the sum of the first 5 5th powers.

4434 is the sum of its proper divisors that contain the digit 7.

4444 is a repdigit.

4480 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4489 is a square whose digits are non-decreasing.

4495 = 31C3.

4498 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4505 is a Zeisel number.

4503 is the largest number that is not the sum of 4 or fewer squares of composites.

4506 is the sum of its proper divisors that contain the digit 5.

4510 = 4444 + 55 + 11 + 0.

4511 = 4444 + 55 + 11 + 1.

4512 = 4444 + 55 + 11 + 2.

4513 = 4444 + 55 + 11 + 3.

4514 = 4444 + 55 + 11 + 4.

4515 = 4444 + 55 + 11 + 5.

4516 = 4444 + 55 + 11 + 6.

4517 = 4444 + 55 + 11 + 7.

4518 = 4444 + 55 + 11 + 8.

4519 = 4444 + 55 + 11 + 9.

4523 has a square in base 2 that is palindromic.

4535 is the number of unlabeled topologies with 7 elements.

4536 is the Stirling number of the first kind s(9,6).

4541 has a square with the first 3 digits the same as the next 3 digits.

4547 is a value of n for which one more than the product of the first n primes is prime.

4548 is the sum of its proper divisors that contain the digit 7.

4552 has a square with the first 3 digits the same as the next 3 digits.

4565 is the number of partitions of 29.

4576 is a truncated tetrahedral number.

4579 is an octahedral number.

4582 is the number of partitions of 52 into distinct parts.

4583 is a value of n for which one less than the product of the first n primes is prime.

4607 is a Woodall number.

4609 = 4444 + 66 + 0 + 99.

4613 is the number of graphs with 10 edges.

4616 has a square comprised of the digits 0-7.

4620 is the largest order of a permutation of 30 or 31 elements.

4624 = 44 + 46 + 42 + 44.

4628 is a Friedman number.

4641 is a rhombic dodecahedral number.

4655 is the number of 10-ominoes.

4665 = 33333 in base 6.

4676 is the sum of the first 7 4th powers.

4681 = 11111 in base 8.

4683 is the number of orderings of 6 objects with ties allowed.

4705 is the sum of consecutive squares in 2 ways.

4713 is a Cullen number.

4734 is the sum of its proper divisors that contain the digit 7.

4750 is a hexagonal pyramidal number.

4752 = (4+4)(4+7)(4+5)(4+2).

4760 is the sum of consecutive squares in 2 ways.

4766 is the number of rooted trees with 12 vertices.

4787 is a value of n for which one more than the product of the first n primes is prime.

4788 is a Keith number.

4793 = 4444 + 7 + 9 + 333.

4804 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4807 is the smallest quasi-Carmichael number in base 10.

4845 = 20C4.

4851 is a pentagonal pyramidal number.

4862 is the 9th Catalan number.

4863 is th! ! e smallest number that cannot be written as the sum of 273 8th powers.

4866 is the number of partitions of 48 in which no part occurs only once.

4890 is the sum of the first 4 6th powers.

4896 = 18P3.

4900 is the only number which is both square! ! and square pyramidal (besides 1).

4901 has a base 3 representation that begins with its base 7 representation.

4913 is the cube of the sum of its digits.

4920 = 6666 in base 9.

4941 is a centered cube number.

4960 = 32C3.

4967 is the number of partitions of 49 in which no part occurs only once.

4974 is the sum of its proper divisors that contain the digit 8.

5000 is the largest number whose English name does not repeat any letters.

5001 appears inside its 4th power.

5002 has a 4th power containing only 4 different digits.

5005 is the smallest palindromic product of 4 consecutive primes.

5010 has a square with the last 3 digits the sam! ! e as the 3 digits before that.

5016 is a heptagonal pyramidal number.

5020 is an amicable number.

5039 is the number of planar partitions of 18.

5040 = 7!

5041 is the largest square known of the form n!+1.

5050 is the sum of the first 100 integers.

5054 = 555 + 0 + 55 + 4444.

5055 has exactly the same digits in 3 different bases.

5100 is divisible by its reverse.

5104 is the smallest number that can be written as the sum of 3 cubes in 3 ways.

5120 is the number of edges in a 10 dimensional hypercube.

5141 is the only four digit number that is reversed in hexadecimal.

5142 is the sum of its proper divisors that contain the digit 7.

5143 = 555 + 111 + 4444 + 33.

5146 has a base 3 representation that begins with its base 7 representation.

5152 is the number of legal rook moves in chess.

5160 = 5! + (1+6)! + 0.

5161 = 5! + (1+6)! + 1!

5162 = 5! + (1+6)! + 2.

5163 = 5! + (1+6)! + 3.

5164 = 5! + (1+6)! + 4.

5165 = 5! + (1+6)! + 5.

5166 = 5! + (1+6)! + 6.

5167 = 5! + (1+6)! + 7.

5168 = 5! + (1+6)! + 8.

5169 = 5! + (1+6)! + 9.

5174 has a 4th power containing only 4 different digits.

5183 is the product of twin primes.

5187 is the only number n known for which phi(n-1) = phi(n) = phi(n+1).

5200 is divisible by its reverse.

5244 is the sum of consecutive squares in 2 ways.

5258 has a base 8 representation which is the reverse of its base! ! 7 representation.

5269 is the number of binary rooted trees with 18 vertices.

5274 is the sum of its proper divisors that contain the digit 7.

5306 is the smallest number whose 9th power starts with 4 identical digits.

5332 is a Kaprekar constant in base 3.

5340 is an octahedral number.

5346 = (198)(27) and each digit is contained in the equation exactly once.

5349 = 12345 in base 8.

5400 is divisible by its reverse.

5434 is the sum of consecutive squares in 2 ways.

5456 and its reverse are tetrahedral numbers.

5460 is the largest order of a permutation of 32 or 33 elements.

5472 has a base 3 representation that ends with its base 4 representation.

5473 has a base 3 representation that ends with its base 4 representation.

5474 is a stella octangula number.

5477 and its reverse are both one more than a square.

5525 is the smallest number that can be written as the sum of 2 squares in 6 ways.

5530 is a hexagonal pyramidal number.

5536 is the 16th tetranacci number.

5555 is a repdigit.

5564 is an amicable number.

5566 is a pentagonal pyramidal number.

5600 is the number of self-complementary graphs with 13 vertices.

5602 = 22222 in base 7.

5604 is the number of partitions of 30.

5610 is divisible by its reverse.

5616 is the order of a non-cyclic simple group.

5673 is the smallest number whose 6th power starts with 5 identical digits.

5682 is the sum of its proper divisors that contain the digit 4.

5693 = 5555 + 6 + 99 + 33.

5696 = 5555 + 66 + 9 + 66.

5698 is the smallest number whose 8th power starts with 5 identical digits.

5700 is divisible by its reverse.

5718 is the number of partitions of 54 into distinct parts.

5719 is a Zeisel number.

5723 has the property that its square starts with its reverse.

5740 = 7777 in base 9.

5768 is the 16th tribonacci number.

5775 is the product of two different substrings of its digits.

5776 is the square of the last half of its digits.

5777 is the smallest number (besides 1) which is not the sum of a prime and twice a square.

5778 is the largest Lucas number which is also a triangular number.

5784 = 555 + 777 + 8 + 4444.

5786 = 5555 + 77 + 88 + 66.

5795 is a Cullen number.

5796 = (138)(42) and each digit is contained in the equation exa! ! ctly once.

5798 is the 11th Motzkin number.

5814 = 19P3.

5822 is the number of conjugacy classes in the automorphism group of the 16 dimensional hypercube.

5823 and its triple contain every digit from 1-9 exactly once.

5830 is an abundant number that is not the sum of some subset of its divisors.

5832 is the cube of the sum of its digits.

5851 is the only prime so that it, its square, and its cube all have the same sum of digits.

5872 = 5555 + 88 + 7 + 222.

5880 is the Stirling number of the second kind S(10,7).

5890 is a heptagonal pyramidal number.

5904 has a square comprised of the digits 1-8.

5906 is the smallest number which is the sum of 2 rational 4th powers but is not the sum of two integer 4th powers.

5913 = 1! + 2! + 3! + 4! + 5! + 6! + 7!

5915 is the sum of consecutive squares in 2 ways.

5923 is the largest n so that Q(n) has class number 7.

5929 is a square which is also the sum of 11 consecutive squares.

5940 is divisible by its reverse.

5963 = 5555 + 9 + 66 + 333.

5968 has ! ! a square comprised of the digits 0-7.

5972 is the smallest number that appears in its factorial 8 times.

5974 is the number of connected planar graphs with 8 vertices.

5984 = 34C3.

5985 = 21C4.

5986 and its prime factors contain every digit from 1-9 exactly once.

5993 is the largest number known which is not the sum of a prime and twice a square.

5994 is the number of lattices on 10 unlabeled nodes.

5995 is a palindromic triangular number.

5996 is a truncated tetrahedral number.

6001 has a cube that is a concatenation of other cubes.

6003 ! ! has a square with the first 3 digits the same as the next 3 digits.

6006 is the smallest palindrome with 5 different prime factors.

6008 = 14C6 + 14C0 + 14C0 + 14C8.

6012 has a square with the last 3 digits the! ! same as the 3 digits before that.

6014 has a square that is formed by 3 squares that overlap by 1 digit.

6020 is the number of Hamiltonian graphs with 8 vertices.

6021 has a square that is formed by 3 squares that overlap by 1 digit.

6048 is the order of a non-cyclic simple group.

6072 is the order of a non-cyclic simple group.

6077 has a square with the last 3 digits the same as the 3 digits before that.

6084 is the sum of the first 12 cubes.

6095 is a rhombic dodecahedral number.

6099 concatenated with its successor is square.

6102 is the largest number n known where phi(n) is the the reverse of n.

6119 is a centered cube number.

6141 is a Kaprekar constant in base 2.

6144 is not the sum of 4 non-zero squares.

6145 is a Friedman number.

6174 is the Kaprekar constant for 4-digit numbers.

6176 is the last 4-digit sequence to appear in the decimal expansion of .

6181 is an octahedral number.

6188 = 17C5.

6200 is a harmonic divisor number.

6216 has a square with the first 3 digits the same as the next 3 digits.

6220 = 44444 in base 6.

6221 = 666 + 2222 + 2222 + 1111.

6223 = 666 + 2222 + 2 + 3333.

6225 = 666 + 2 + 2 + 5555.

6232 is an amicable number.

6248 is the smallest number with the property that its first 8 multiples contain the digit 4.

6249 is the smallest number with the property that its first 10 multiples contain the digit 4.

6257 is the number of essentially different ways to dissect a 20-gon into 9 quadrilaterals.

6296 has a square with the first 3 digits the same as the next 3 digits.

6300 is divisible by its reverse.

6307 is the largest n s! ! o that Q(n) has class number 8.

6312 is the sum of its proper divisors that contain the digit 5.

6318 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

6348 is a pentagonal pyramidal number.

6368 is an amicable number.

6375 has a square with the first 3 digits the same as the next 3 digits.

6378 is the number of partitions of 55 into distinct parts.

6380 is a value of n for which n!+1 is prime.

6389 is the number of functional graphs on 11 vertices.

6391 is a hexagonal pyramidal number.

6400 is a square whose digits are non-increasing.

6403 has a square with the first 3 digits the same as the last 3 digits.

6404 is a value of n for which n!! – 1 is prime.

6435 = 15C7.

6444 is the smallest number whose 5th power starts with 5 identical digits.

6455 is a strong Friedman number.

6487 is the number of partitions of 51 in which no part occurs only once.

6489 is half again as large as the sum of its proper divisors.

6500 is a number n whose sum of the factorials of its digits is equal to pi(n).

6501 has a square whose reverse is also a square.

6510 is a number n whose sum of the factorials of its digits is equal to pi(n).

6511 is a number n whose sum of the factorials of its digits is equal to pi(n).

6521 is a number n whose sum of the factorials of its digits is equal to pi(n).

6523 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

6524 has the property that its square starts with its reverse.

6526 is the smallest number whose 10th power contains exactly the same digits as another 10th power.

6545 and its reverse are tetrahedral numbers.

6556 is the largest palindrome that can be made using 5 digits and the 4 arithmetic operations.

6560 is the smallest number n where n and n+1 are both products of 7 or more primes.

6561 = 38.

6569 is a value of n for which one less than the product of the first n primes is prime.

6572 is the number of 9-hexes.

6578 is the smallest number which can be written as the sum of 3 4th powers in 2 ways.

6588 is the number of sided 12-iamonds.

6593 = 6 + 5555 + 999 + 33.

6596 has a square comprised of the digits 0-7.

6601 is a Carmichael number.

6603 is a number whose square and cube use different digits.

6611 is a Cullen number.

6620 is the number of 11-ominoes that tile the plane.

6636 has exactly the same digits in 3 different bases.

6643 is the smallest number which is palindromic in bases 2 and 3.

6666 is a repdigit.

6667 is the number of self-dual planar graphs with 24 edges.

6680 = 6666 + 6 + 8 + 0.

6681 = 6666 + 6 + 8 + 1.

6682 = 6666 + 6 + 8 + 2.

6683 = 6666 + 6 + 8 + 3.

6684 = 6666 + 6 + 8 + 4.

6685 = 6666 + 6 + 8 + 5.

6686 = 6666 + 6 + 8 + 6.

6687 = 6666 + 6 + 8 + 7.

6688 = 6666 + 6 + 8 + 8.

6689 = 6666 + 6 + 8 + 9.

6720 = 8P5.

6729 and its double together use each of the digits 1-9 exactly once.

6735 is a stella octangula number.

6742 has a square where the first 6 digits alternate.

6765 is the 20th Fibonacci number.

6769 is the Stirling number of the first kind s(8,4).

6772 = 6666 + 7 + 77 + 22.

6779 = 6666 + 7 + 7 + 99.

6788 is the smallest number with multiplicative persistence 6.

6789 is the largest 4-digit number with increasing digits.

6840 = 20P3.

6842 is the number of partitions of 31.

6859 = 193.

6860 is a heptagonal pyramidal number.

6864 = 6666 + 88 + 66 + 44.

6880 is a vamp! ! ire number.

6888 has a square with 3/4 of the digits are the same.

6889 is a strobogrammatic square.

6912 = (6) (9) (1) (2)7.

6922 is the number of polycubes containing 8 cubes.

6930 is the square root of a triangular number.

6940 is the sum of its proper divisors that contain the digit 3.

6941 has a square with the first 3 digits the same as the last 3 digits.

6942 is the number of labeled topologies with 5 elements.

6951 has exactly the same digits in 3 different bases.

6952 = (1738)(4) and each digit is contained in the equation exactly once.

6953 = 66 + 999 + 5555 + 333.

6966 is! ! the number of planar graphs with 8 vertices.

7014 has a square with the last 3 digits the same as the 3 digits before that.

7106 is an octahedral number.

7108 is the number of partitions of 56 into distinct parts.

7123 is the number of 2-connected graphs with 8 vertices.

7140 is the largest number which is both triangular and tetrahedral.

7145 has a square with the first 3 digits the same as the next 3 digits.

7152 has a square with! ! the first 3 digits the same as the next 3 digits.

7159 has a square with the first 3 digits the same as the next 3 digits.

7161 is a Kaprekar constant in base 2.

7192 is an abundant number that is not the sum of some subset of its divisors.

7200 is a pentagonal pyramidal number.

7230 is the sum of consecutive squares in 2 ways.

7245 appears inside its 4th power.

7254 = (186)(39) and each digit is contained in the equation exactly once.

7272 is a Kaprekar number.

7306 is the smallest number whose 7th power starts with 7 identical digits.

7314 is the smallest number so that it and its successor are both products of 4 primes.

7315 = 22C4.

7318 is the number of functions from 10 unlabeled! ! points to themselves.

7351 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7360 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7337 is a hexagonal pyramidal number.

7371 has a base 2 representation that begins with its base 9 representation.

7381 = 11111 in base 9.

7385 is a Keith number.

7422 is the sum of its proper divisors that contain the digit 7.

7429 is the ! ! product of 3 consecutive primes.

7436 is the number of 6×6 alternating sign matrices.

7448 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7465 = 54321 in base 6.

7471 is a centered cube number.

7490 has a square with the last 3 digits the same as the 3 digits before that.

7491 has a base 8 representation which is the reverse of its base 7 representation.

7494 is the sum of its proper divisors that contain the digit 4.

7496 = 777 + 44 + 9 + 6666.

7512 is the sum of its proper divisors that contain the digit 5.

7525 has a square with the last 3 digits the same as the 3 digits before that.

7532 has a square comprised of the digits 0-7.

7549 is the largest known prime p where no numbers of the form p-n2 are prime.

7560 is the smallest number with 64 divisors.

7574 is the sum of consecutive squares in 2 ways.

7581 is the number of monotone Boolean functions of 5 variables.

7586 = 777 + 55 + 88 + 6666.

7595 is the number of simplicial polyhedra with 12 vertices.

7647 is a Keith number.

7663 is the product of two primes which are reverses of each other.

7665 is a Kaprekar constant in base 2.

7672 = 777 + 6666 + 7 + 222.

7673 is the smallest number with the property that its first 8 multiples contain the digit 3.

7679 = 7 + 6666 + 7 + 999.

7683 is a truncated tetrahedral number.

7693 is a value of n for which the sum of the first n primes is a palindrome.

7698 has a square with the first 3 digits the same as the next 3 digits.

7710 is the number of degree 17 irreducible polynomials over GF(2).

7734 is the sum of its proper divisors that contain the digit 8.

7741 is the number of trees with 15 vertices.

7744 is the only square known with no isolated digits.

7745 and its reverse are both one more than a square.

7770 = 37C3.

7775 = 55555 in base 6.

7776 is a 5th power whose digits are non-increasing.

7777 is a Kaprekar number.

7800 is the order of a non-cyclic simple group.

7810 has the property that its square is the concatenation of two consecutive numbers.

7812 = 222222 in base 5.

7825 is a rhombic dodecahedral number.

7851 = 7777 + 8 + 55 + 11.

7852 = (1963)(4) and each digit is contained in the equation exactly once.

7856 = 7777 + 8 + 5 + 66.

7905 is a Kaprekar constant in base 2.

7909 is a Keith number.

7917 is the number of partitions of 57 into distinct parts.

7920 is the order of the smallest sporadic group.

7928 is a Friedman number.

7931 is a heptagonal pyramidal number.

7936 is the 9th Euler number.

7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7969 has a square that is formed by 3 squares that overlap by 1 digit.

7980 is the smallest number whose divisors contain every digit at least 7 times.

7993 is one less than twice its reverse.

8000 is the smallest cube which is also the sum of 4 consecutive cubes.

8001 is a Kaprekar constant in base 2.

8004 has a square with the first 3 digits the same as the next 3 digits.

8008 = 16C6.

8016 has a square with the last 3 digits the same as the 3 digits before that.

8026 is the number of planar partitions of 19.

8042 is the largest number known which cannot be written as a sum of 7 or fewer cubes.

8051 is the number of partitions of 52 in which no part occurs only once.

8071 is the number of connected graphs with 11 edges.

8082 has a square comprised of the digits 1-8.

8092 is a Friedman number.

8100 is divisible by its reverse.

8119 is an octahedral number.

8125 is the smallest number that can be written as the sum of 2 squares in 5 ways.

8128 is the 4th perfect number.

8136 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

8176 is a stella octangula number.

8184 has exactly the same digits in 3 different bases.

8190 is a harmonic divisor number.

8191 is a Mersenne prime.

8192 is the smallest 13th power (besides 1).

8200 = 8 + 213 + 0 + 0.

8201 = 8 + 213 + 0 + 1.

8202 = 8 + 213 + 0 + 2.

8203 = 8 ! ! + 213 + 0 + 3.

8204 = 8 + 213 + 0 + 4.

8205 = 8 + 213 + 0 + 5.

8206 = 8 + 213 + 0 + 6.

8207 = 8 + 213 + 0 + 7.

8208 = 84 + 24 + 04 + 84.

8209 = 8 + 213 + 0 + 9.

8221 has a base 3 representation that begins with its base 6 representation.

8226 is the sum of its proper divisors that contain the digit 4.

8281 is the only 4-digit square whose two 2-digit pairs are consecutive.

8283 has a base 8 representation which is the reverse of its base 7 representation.

8303 = 12345 in base 9.

8342 is the number of partitions of 53 in which no part occurs only once.

8349 is the number of partitions of 32.

8372 is a hexagonal pyramidal number.

8375 is the smallest number which has equal numbers of every digit in bases 2 and 6.

8384 is the maximum number of 13th powers needed to sum to any number.

8400 is the number of legal queen moves in chess.

8403 = 33333 in base 7.

8415 is the smallest number which has equal numbers of every digit in bases 3 and 6.

8436 = 38C3.

8461 is the smallest number whose 9th power starts with 5 identical digits.

8470 is the number of conjugacy classes in the automorphism group of the 17 dimensional hypercube.

8486 = 888 + 44 + 888 + 6666.

8510 is a value of n for which the sum of the first n primes is a palindrome.

8515 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

8538 is the sum of its proper divisors that contain the digit 4.

8559 has a square comprised of the digits 1-8.

8562 is the sum of its proper divisors that contain the digit 4.

8568 = 18C5.

8578 appears inside its 4th power.

8586 has exactly the same digits in 3 different bases.

8614 and its prime factors contain every digit from 1-9 exactly once.

8664 = 888 + 6666 + 666 + 444.

8670 is a value of n fo! ! r which n!! – 1 is prime.

8680 has a base 5 representation that ends with its base 7 representation.

8681 has a base 5 representation that ends with its base 7 representation.

8682 has a base 5 representation that ends with its base 7 representation.

8683 has a base 5 representation that ends with its base 7 representation.

8684 has a base 5 representation that ends with its base 7 representation.

8712 is 4 times its reverse.

8714 is the number of ways 24 people around a round table can shake hands in a non-crossing way, up to rotation.

8732 has exactly the same digits in 3 different bases.

8736 is the smallest number that appears in its factorial 10 times.

8753 = 88 + 7777 + 555 + 333.

8758 = 88 + 7777 + 5 + 888.

8763 and its successor have the same digits in their prime factorization.

8772 is the sum of the first 8 4th powers.

8778 is a palindromic triangular number.

8808 is the number of partitions of 58 into distinct parts.

8826 is the sum of its proper divisors that contain the digit 4.

8833 = 882 + 332.

8855 = 23C4.

8888 is a repdigit.

8910 is divisible by its reverse.

8911 is a Carmichael number.

8922 is the sum of its proper divisors that contain the digit 4.

8930 = 8888 + 9 + 33 + 0.

8931 = 8888 + 9 + 33 + 1.

8932 = 8888 + 9 + 33 + 2.

8933 = 8888 + 9 + 33 + 3.

8934 = 8888 + 9 + 33 + 4.

8935 = 8888 + 9 + 33 + 5.

8936 = 8888 + 9 + 33 + 6.

8937 = 8888 + 9 + 33 + 7.

8938 = 8888 + 9 + 33 + 8.

8939 = 8888 + 9 + 33 + 9.

8964 is the smallest number with the proper! ! ty that its first 6 multiples contain the digit 8.

8970 = 8 + 94 + 74 + 0.

8971 = 8 + 94 + 74 + 1.

8972 = 8 + 94 + 74 + 2.

8973 = 8 + 94 + 74 + 3.

8974 = 8 + 94! ! + 74 + 4.

8975 = 8 + 94 + 74 + 5.

8976 = 8 + 94 + 74 + 6.

8977 = 8 + 94 + 74 + 7.

8978 = 8 + 94 + 74 + 8.

8979 = 8 + 94 + 74! ! + 9.

8991 is the smallest number so that it and its successor are both the product of a prime and the 5th power of a prime.

9009 is a centered cube number.

9012 is the sum of its proper divisors that contain the digit 5.

9018 has a square with the last 3 digits the same as the 3 digits before that.

9024 has a square comprised of the digits 1-8.

9025 is a Friedman number.

9072 has a base 2 and base 3 representation that end with its base 6 representation.

9073 has a base 2 and base 3 representation that end with its base 6 representation.

9074 has a base 3 representation that ends with its base 6 representation.

9091 is the only prime known whose reciprocal has period 10.

9093 has a square with the first 3 digits the same as the next 3 digits.

9101 has a square where the first 6 digits alternate.

9104 has a square with the first 3 digits the same as the next 3 digits.

9108 is a heptagonal pyramidal number.

9115 has a base 3 representation that begins with its base 6 representation.

9126 is a pentagonal pyramidal number.

9139 = 39C3.

9174 is the sum of its proper divisors that contain the digit 5.

9189 is the number of sided 10-ominoes.

9216 is a Friedman number.

9224 is an octahedral number.

9233 is the number of different arrangements (up to rotation and reflection) of 13 non-attacking queens on a 13×13 chessboard.

9235 has a square with the first 3 digits the same as the next 3 digits.

9240 = 22P3.

9253 is the smallest number that appears in its factorial 9 times.

9261 is a Friedman number.

9272 is an abundant numbe! ! r that is not the sum of some subset of its divisors.

9330 is the Stirling number of the second kind S(10,3).

9331 = 111111 in base 6.

9349 is the 19th Lucas number.

9350 appears inside its 4th power.

9362 = 22222 in base 8.

9376 is an automorphic number.

9377 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

9385 is the sum of consecutive squares in 2 ways.

9386 = 99 + 333 + 8888 + 66.

9391 has a square with the first 3 digits the same as the last 3 digits.

9408 is the number of reduced 6 x 6 Latin squares.

9436 is the smallest number whose 15th power contains exactly the same digits as another 15th power.

9444 has a square with the first 3 digits the same as the next 3 digits.

9451 is the number of binary rooted trees with 19 vertices.

9468 is the sum of its proper divisorsproper divisors that contain the digit 7.

9474 = 94 + 44 + 74 + 44.

9477 is the maximum determinant of a 13 x 13 matrix of 0’s and 1’s.

9496 is the number of 10×10 symmetric permutation matrices.

9500 is a hexagonal pyrami! ! dal number.

9563 = 9 + 5555 + 666 + 3333.

9568 = 9 + 5 + 666 + 8888.

9608 is the number of digraphs with 5 vertices.

9615 is the smallest number whose cube starts with 5 identical digits.

9625 has a square formed by inserting a block of digits inside itself.

9653 = 99 + 666 + 5555 + 3333.

9658 = 99 + 666 + 5 + 8888.

9660 is a truncated tetrahedral number.

9682 is a value of n for which! ! n!! – 1 is prime.

9689 is the exponent of a Mersenne prime.

9726 is the smallest number in base 5 whose square contains the same digits in the same proportion.

9784 is the number of 2 state Turing machines which halt.

9789 is the smallest number that appears in its factorial 11 times.

9792 is the number of partitions of 59 into distinct parts.

9801 is 9 times its reverse.

9809 is a stella octangula number.

9828 is the orde! ! r of a non-cyclic simple group.

9831 has a base 6 representation which is the reverse of its base 5 representation.

9841 = 111111111 in base 3.

9855 is a rhombic dodecahedral number.

9862 is the number of knight’s tours on a 6 x 6 chess board.

9876 is the largest 4-digit number with different digits.

9880 = 40C3.

9901 is the only prime known whose reciprocal has period 12.

9941 is the exponent of a Mers! ! enne prime.

9973 is the largest 4-digit prime.

9976 has a square formed by inserting a block of digits inside itself.

9988 is the number of prime knots with 13 crossings.

9995 has a square formed by inserting a block of digits inside itself.

9996 has a square formed by inserting a block of digits inside itself.

9999 is a Kaprekar number.

3. 