252 (number)

252 (two hundred [and] fifty-two) is the natural number following 251 and preceding 253.

252 is the central binomial coefficient $\tbinom{10}{5}$, and is $\tau(3)$, where $\tau$ is the Ramanujan tau function. 252 is also $\sigma_3(6)$, where $\sigma_3$ is the function that sums the cubes of the divisors of its argument:

$1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252.$

It is a practical number, and a hexagonal pyramidal number. There are 252 points on the surface of a cuboctahedron of radius five in the fcc 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, and 252 ways of placing four pieces on a Connect Four board.