252 (number)
# 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 4×4 chessboard up to reflections and rotations, and 252 ways of placing three pieces on a Connect Four board.

