252 (number)

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

In mathematics

252 is:

• the central binomial coefficient $(\genfrac{}{}{0ex}{}{10}{5})$, 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.