What numbers are almost perfect numbers?

Answer 1

Almost perfect numbers refer to numbers where

σ(x) = 2x - 1, where σ is the sum of divisors function. Any number in the form 2n is almost perfect because

σ(2n) = 1 + 2 + 4 + ... + 2n = 2n+1-1 = 2(2n) - 1.

It is unknown whether any other almost perfect numbers exist.