In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function σ(n)) is equal to 2n + 1.
If a quasiperfect number exists, it must be an odd square number greater than 1035 and have at least seven distinct prime factors.
[1] For a perfect number n the sum of all its divisors is equal to 2n.
For an almost perfect number n the sum of all its divisors is equal to 2n - 1.
(OEIS A088831) Numbers n exist whose sum of factors = 2n - 2.