52 (number)

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title: "52 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["integers"] topic_path: "general/integers" source: "https://en.wikipedia.org/wiki/52_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::data[format=table title="Infobox number"]

FieldValue
number52
divisor1, 2, 4, 13, 26, 52
::

| number = 52 | divisor = 1, 2, 4, 13, 26, 52 52 (fifty-two) is the natural number following 51 and preceding 53.

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, |title=Bell, or exponential numbers |id=Sloane's A000110 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation (oeis.org) |url=https://oeis.org/A000110 |access-date=2016-05-30 |df=dmy-all the number of ways to partition a set of 5 objects.
  • a decagonal number. |title=10-gonal (or decagonal) numbers |id=Sloane's A001107 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation (oeis.org) |url=https://oeis.org/A001107 |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. |title=Untouchable numbers |id=Sloane's A005114 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation (oeis.org) |url=https://oeis.org/A005114 |access-date=2016-05-30 |df=dmy-all
  • a noncototient since it is not equal to x − φ(x) for any |title=Noncototients |id=Sloane's A005278 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation (oeis.org) |url=https://oeis.org/A005278 |access-date=2016-05-30 |df=dmy-all
  • a vertically symmetrical number. |title=Vertically symmetric numbers |id=Sloane's A053701 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation (oeis.org) |url=https://oeis.org/A053701 |access-date=2022-05-08 |df=dmy-all

In other fields

::figure[src="https://upload.wikimedia.org/wikipedia/commons/e/e5/Piano_keyboard.JPG" caption="A full-size [[piano]] has 52 white keys, out of 88 total keys."] ::

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

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::

integers