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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 p · q , where q is some prime larger than p . It is the sixth of this form and the fifth of the form 2 · q .
• the 5th Bell number, the number of ways to partition a set of 5 objects.
• a decagonal number.
• 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.
• a noncototient since it is not equal to x − φ(x) for any x .
• 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

1. "Bell, or exponential numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation (oeis.org). Sloane's A000110. Retrieved 30 May 2016.
2. "10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation (oeis.org). Sloane's A001107. Retrieved 30 May 2016.
3. "Untouchable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation (oeis.org). Sloane's A005114. Retrieved 30 May 2016.
4. "Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation (oeis.org). Sloane's A005278. Retrieved 30 May 2016.
5. "Vertically symmetric numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation (oeis.org). Sloane's A053701. Retrieved 8 May 2022.

• Integers