Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)

PerfectNumber

PerfectNumber[n]
gives the n^(th) perfect number.

DetailsDetails

  • A perfect number is a positive integer that is equal to half the sum of its divisors.
  • In PerfectNumber[n], n must be a positive integer.
  • As of this version of the Wolfram Language, only 49 perfect numbers are known. PerfectNumber[n] will attempt to find perfect numbers for any n, but cannot be expected to return results in a reasonable time for .
  • PerfectNumber[n,"Even"] gives the n^(th) even perfect number. As of this version of the Wolfram Language, the first 44 even perfect numbers are known, and 5 more whose position n is not yet certain. PerfectNumber[n,"Even"] will attempt to find even perfect numbers for , but cannot be expected to return results in a reasonable time.
  • PerfectNumber[n,"Odd"] will attempt to find the n^(th) odd perfect number. As of this version of the Wolfram Language, no odd perfect number is known, and PerfectNumber[n,"Odd"] cannot be expected to return a result. There are no odd perfect numbers less than the 18^(th) even perfect number.
Introduced in 2016
(10.4)