In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1. Quasiperfect numbers are abundant numbers. No quasiperfect numbers have been found so far, but it has been shown that if any quasiperfect numbers exist, they must be greater than 1035 and have at least seven divisors.