Quasiperfect Number

A least Abundant Number, i.e., one such that

$$\sigma(n)=2n+1.$$

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 Divisors. Singh (1997) called quasiperfect numbers Slightly Excessive Numbers.

See also Abundant Number, Almost Perfect Number, Perfect Number

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.

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