52 (fifty-two) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
51 and preceding
53.
In mathematics
Fifty-two is
* a
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
; a square-prime, of the form where is some prime larger than It is the sixth of this form and the fifth of the form
* the 5th
Bell number, the number of ways to partition a set of 5 objects.
* a
decagonal number.
* with an
aliquot sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself.
That is,
s(n)=\sum_ d \, .
It can be used to characterize the prime numbers, perfect numbers, sociabl ...
of
46; within an
aliquot sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Def ...
of seven composite numbers to the prime in the
3-aliquot tree. This sequence does not extend above 52 because it is,
* an
untouchable number, since it is never the sum of
proper divisors of any number. It is the first untouchable number larger than 2 and 5.
* a
noncototient
In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function
In number theory ...
since it is not equal to for any
* a vertically symmetrical number.
[
]
In other fields
Fifty-two is:
* The number of cards in a standard deck of
playing cards, not counting
Jokers or advertisement cards
References
{{Integers, zero
Integers