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'{{Infobox number | number = 252 | divisor = 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252 }} '''252''' ('''two hundred [and] fifty-two''') is the [[natural number]] following [[251 (number)|251]] and preceding [[253 (number)|253]]. ==In mathematics== '''252''' is: *the [[central binomial coefficient]] <math>\tbinom{10}{5}</math>, the largest one divisible by all coefficients in the previous line<ref>{{Cite OEIS|A000984|name=Central binomial coefficients}}</ref> *a [[Harshad number]] in base 10. *<math>\tau(3)</math>, where <math>\tau</math> is the [[Ramanujan tau function]].<ref>{{Cite OEIS|A000594|name=Ramanujan's tau function}}</ref> *<math>\sigma_3(6)</math>, where <math>\sigma_3</math> is the [[Divisor function|function that sums the cubes of the divisors]] of its argument:<ref>{{Cite OEIS|A001158|name=sigma_3(n): sum of cubes of divisors of n}}</ref> :<math>1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252.</math> *a [[practical number]],<ref>{{Cite OEIS|A005153|name=Practical numbers}}</ref> *a [[refactorable number]],<ref>{{Cite web|url=https://oeis.org/A033950|title=Sloane's A033950 : Refactorable numbers|date=2016-04-18|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-04-18}}</ref> *a [[hexagonal pyramidal number]].<ref>{{Cite OEIS|A002412|name=Hexagonal pyramidal numbers, or greengrocer's numbers}}</ref> *a member of the [[Mian–Chowla sequence|Mian-Chowla sequence]].<ref>{{Cite web|url=https://oeis.org/A005282|title=Sloane's A005282 : Mian-Chowla sequence|date=2016-04-19|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-04-19}}</ref> There are 252 points on the surface of a [[cuboctahedron]] of radius five in the [[FCC close packing|face-centered cubic]] lattice,<ref>{{Cite OEIS|A005901|name=Number of points on surface of cuboctahedron}}</ref> 252 ways of writing the number 4 as a sum of six squares of integers,<ref>{{Cite OEIS|A000141|name=Number of ways of writing n as a sum of 6 squares}}</ref> 252 ways of choosing four squares from a 4&times;4 chessboard up to reflections and rotations,<ref>{{Cite OEIS|A019318|name=Number of inequivalent ways of choosing n squares from an n X n board, considering rotations and reflections to be the same}}</ref> and 252 ways of placing three pieces on a [[Connect Four]] board.<ref>{{Cite OEIS|A090224|name=Number of possible positions for n men on a standard 7 X 6 board of Connect-Four}}</ref> ==References== {{reflist}} {{Integers|2}} [[Category:Integers]] {{number-stub}}'