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Weird Number

A number which is Abundant without being Semiperfect. (A Semiperfect Number is the sum of any set of its own Divisors.) The first few weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, ... (Sloane's A006037). No Odd weird numbers are known, but an infinite number of weird numbers are known to exist. The Sequence of weird numbers has Positive Schnirelmann Density.

See also Abundant Number, Schnirelmann Density, Semiperfect Number


Benkoski, S. ``Are All Weird Numbers Even?'' Amer. Math. Monthly 79, 774, 1972.

Benkoski, S. J. and Erdös, P. ``On Weird and Pseudoperfect Numbers.'' Math. Comput. 28, 617-623, 1974.

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 A006037/M5339 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein