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In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ1(n) = 2n.

All even perfect numbers are of the form 2p−1(2p − 1) with prime p, except 6 and 24, all even perfect numbers end with 54, all even perfect numbers are also triangular numbers.