slightly excessive number

A quasiperfect number, called a "slightly excessive number" by Singh, is a "least" abundant number, i.e., one such that σ(n) = 2n + 1. Quasiperfect numbers are therefore the sum of their nontrivial divisors. No quasiperfect numbers are known, although if any exist, they must be greater than 10^35 and have seven or more distinct prime factors.

abundant number | almost perfect number | perfect number