252 (number)

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

In mathematics
252 is:
 * the central binomial coefficient $$\tbinom{10}{5}$$, the largest one divisible by all coefficients in the previous line
 * $$\tau(3)$$, where $$\tau$$ is the Ramanujan tau function.
 * $$\sigma_3(6)$$, where $$\sigma_3$$ is the function that sums the cubes of the divisors of its argument:
 * $$1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252.$$


 * 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&times;4 chessboard up to reflections and rotations, and 252 ways of placing three pieces on a Connect Four board.