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.
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