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Articles: Education/Training | Something abt numbers...........
- Ms. Nayana D
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Mind Blowing.....................
0 s the additive identity.
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 9x9 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 triangular 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 8x8 chess board.
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 which 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 known 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 the 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 the 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 7x7 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 4x8 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 smallest 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 4x4 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 9x9 chess board.
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 of 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 pyramidal 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 its 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 different arrangements of 10 non-attacking queens on an 10x10 chess board.
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 8x8 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
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