252 (two hundred
ndfifty-two) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called '' cardinal ...
following
251 and preceding
253
__NOTOC__
Year 253 ( CCLIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Volusianus and Claudius (or, less frequently, year 100 ...
.
In mathematics
252 is:
*the
central binomial coefficient
In mathematics the ''n''th central binomial coefficient is the particular binomial coefficient
: = \frac = \prod\limits_^\frac \textn \geq 0.
They are called central since they show up exactly in the middle of the even-numbered rows in Pascal ...
, the largest one divisible by all coefficients in the previous line
*
, where
is the
Ramanujan tau function
The Ramanujan tau function, studied by , is the function \tau : \mathbb \rarr\mathbb defined by the following identity:
:\sum_\tau(n)q^n=q\prod_\left(1-q^n\right)^ = q\phi(q)^ = \eta(z)^=\Delta(z),
where with , \phi is the Euler function, is th ...
.
*
, where
is the
function that sums the cubes of the divisors of its argument:
:
*a
practical number
In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 ...
,
*a
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as
: 1, 2, 8, 9, 12, 18, ...
,
*a
hexagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...
.
*a member of the
Mian-Chowla sequence.
There are 252 points on the surface of a
cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it ...
of radius five in the
face-centered cubic
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.
There are three main varieties of ...
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
Connect Four (also known as Connect 4, Four Up, Plot Four, Find Four, Captain's Mistress, Four in a Row, Drop Four, and Gravitrips in the Soviet Union) is a two-player connection board game, in which the players choose a color and then take tur ...
board.
References
Integers
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