Weird Number

A number which is Abundant without being Semiperfect. (ASemiperfect 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 numberof weird numbers are known to exist. The Sequence of weird numbers has Positive Schnirelmann Density.

References

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. SequenceA006037/M5339in ``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.

• Whitney Umbrella
• Whittaker Differential Equation
• Whittaker Function
• Whole Number
• Width (Partial Order)
• Width (Size)
• Wiedersehen Manifold
• Wieferich Prime
• Wielandt's Theorem
• Wiener Filter
• Wiener Function
• Wiener-Khintchine Theorem
• Wiener Measure
• Wiener Space
• Wigner 3j-Symbol
• Wigner 6j-Symbol
• Wigner 9j-Symbol
• Wigner-Eckart Theorem
• Wilbraham-Gibbs Constant
• Wilcoxon Rank Sum Test
• Wilcoxon Signed Rank Test
• Wild Knot
• Wild Point
• Wilf-Zeilberger Pair
• Wilkie's Theorem