252 (two hundred [and] fifty-two) is the natural number following 251 and preceding 253.
In mathematics 252 is:
the central binomial coefficient ( 10 5 ) {\displaystyle {\tbinom {10}{5}}} , the largest one divisible by all coefficients in the previous line
τ ( 3 ) {\displaystyle \tau (3)} , where τ {\displaystyle \tau } is the Ramanujan tau function.
σ 3 ( 6 ) {\displaystyle \sigma _{3}(6)} , where σ 3 {\displaystyle \sigma _{3}} is the function that sums the cubes of the divisors of its argument:
1 3 + 2 3 + 3 3 + 6 3 = ( 1 3 + 2 3 ) ( 1 3 + 3 3 ) = 252. {\displaystyle 1^{3}+2^{3}+3^{3}+6^{3}=(1^{3}+2^{3})(1^{3}+3^{3})=252.}
a practical number, a refactorable number, a hexagonal pyramidal number. a member of the Mian-Chowla sequence. There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice, 252 ways of writing the number 4 as a sum of six squares of integers, 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations, 252 ways of placing three pieces on a Connect Four board, and 252 possible dice combinations in the game Yahtzee.
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