Quasiperfect Number

A quasiperfect number, called a "slightly excessive number" by Singh (1997), is a "least" abundant number, i.e., one such that

Quasiperfect numbers are therefore the sum of their nontrivial divisors. No quasiperfect numbers are known, although if any exist, they must be greater than  and have seven or more distinct prime factors (Hagis and Cohen 1982).

REFERENCES:

Guy, R. K. "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." §B2 in Unsolved Problems in Number Theory, 2nd ed. New York:Springer-Verlag, pp. 45-53, 1994.

Hagis, P.; and Cohen, G. L. "Some Results Concerning Quasiperfect Numbers." J. Austral. Math. Soc. Ser. A 33, 275-286, 1982.

Singh, S. Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. New York: Walker, p. 13, 1997.