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

It seems to be an open problem to show that a number is almost perfect only if it is of the form .

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."