52 (number)

In mathematics

Fifty-two is

• a composite number; a square-prime, of the form where q is some prime larger than It is the sixth of this form and the fifth of the form
• the 5th Bell number, |access-date=2016-05-30 |df=dmy-all the number of ways to partition a set of 5 objects.
• a decagonal number. |access-date=2016-05-30 |df=dmy-all
• with an aliquot sum of 46; within an aliquot sequence of seven composite numbers { 52, 46, 26, 16, 15, 9, 4, 3, 1, 0} 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. |access-date=2016-05-30 |df=dmy-all
• a noncototient since it is not equal to x − φ(x) for any |access-date=2016-05-30 |df=dmy-all
• a vertically symmetrical number. |access-date=2022-05-08 |df=dmy-all

In other fields

Fifty-two is:

• The number of cards in a standard deck of playing cards, not counting Jokers or advertisement cards
• The number of weeks in a calendar year
• The number of white keys on a piano

References