A number such as which is the Sum of some (or all) of its Proper Divisors. A
semiperfect number which is the Sum of *all* its Proper Divisors is called a
Perfect Number. The first few semiperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40, ... (Sloane's A005835).
Every multiple of a semiperfect number is semiperfect, as are all numbers for and a Prime
between and (Guy 1994, p. 47).

A semiperfect number cannot be Deficient. Rare Abundant Numbers which are not semiperfect are called Weird Numbers. Semiperfect numbers are sometimes also called Pseudoperfect Numbers.

**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.

Sloane, N. J. A. Sequence
A005835/M4094
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.

Zachariou, A. and Zachariou, E. ``Perfect, Semi-Perfect and Ore Numbers.'' *Bull. Soc. Math. Gréce (New Ser.)*
**13**, 12-22, 1972.

© 1996-9

1999-05-26