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Almost Perfect Number

An almost perfect number, also known as a least deficient or slightly defective (Singh 1997) number, is a positive integer n for which the divisor function satisfies sigma(n)=2n-1. The only known almost perfect numbers are the powers 2^k for nonnegative integers k, namely 1, 2, 4, 8, 16, 32, ... (OEIS A000079).

It remains an open problem whether every almost perfect number is a power of 2.

See also

Deficient Number, Perfect Number, Quasiperfect Number

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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. 16 and 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.Sloane, N. J. A. Sequence A000079/M1129 in "The On-Line Encyclopedia of Integer Sequences."

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Almost Perfect Number

Cite this as:

Weisstein, Eric W. "Almost Perfect Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlmostPerfectNumber.html

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