A number for which the Divisor Function satisfies is called almost perfect. The only known almost perfect numbers are the Powers of 2, namely 1, 2, 4, 8, 16, 32, ... (Sloane's A000079). Singh (1997) calls almost perfect numbers Slightly Defective.

**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 ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-25