Semiperfect Number
A number such as 
which is the Sum of some (or all) of its Proper Divisors. Asemiperfect number which is the Sum of all its Proper Divisors is called aA005835). Every multiple of a semiperfect number is semiperfect, as are all numbers 
for 
and 
a Primebetween 
and 
(Guy 1994, p. 47).
A semiperfect number cannot be Deficient. Rare Abundant Numberswhich are not semiperfect are called Weird Numbers. Semiperfect numbers are sometimes also called Pseudoperfect Numbers.
See also Abundant Number, Deficient Number, Perfect Number, Primitive Semiperfect Number, WeirdNumber
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. SequenceA005835/M4094in ``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.
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