Determine whether a number equals the sum of its proper divisors.
A perfect number equals the sum of its proper divisors (all divisors except itself). The first four perfect numbers are 6, 28, 496 and 8128. All known even perfect numbers have the form 2^(p−1) × (2^p − 1) where 2^p − 1 is a Mersenne prime. Whether odd perfect numbers exist is an open problem.
Perfect number definition
n is perfect ⟺ σ(n) − n = n ⟺ σ(n) = 2n
6 (1+2+3), 28 (1+2+4+7+14), 496, and 8128. The fifth is 33,550,336.
A number whose proper divisors sum to more than itself. For example, 12 is abundant because 1+2+3+4+6 = 16 > 12. A number with divisor sum less than itself is called deficient.