On weird and pseudoperfect numbers

Authors:
S. J. Benkoski and P. Erdős

Journal:
Math. Comp. **28** (1974), 617-623

MSC:
Primary 10A40

DOI:
https://doi.org/10.1090/S0025-5718-1974-0347726-9

Corrigendum:
Math. Comp. **29** (1975), 673-674.

Corrigendum:
Math. Comp. **29** (1975), 673.

MathSciNet review:
0347726

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Abstract | References | Similar Articles | Additional Information

Abstract: If *n* is a positive integer and $\sigma (n)$ denotes the sum of the divisors of *n*, then *n* is perfect if $\sigma (n) = 2n$, abundant if $\sigma (n) \geqq 2n$ and deficient if $\sigma (n) < 2n$. *n* is called pseudoperfect if *n* is the sum of distinct proper divisors of *n*. If *n* is abundant but not pseudoperfect, then *n* is called weird. The smallest weird number is 70. We prove that the density of weird numbers is positive and discuss several related problems and results. A list of all weird numbers not exceeding ${10^6}$ is given.

- Stan Benkoski,
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*J. London Math. Soc.*, v. 10, 1935, pp. 49-58.

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Keywords:
Weird numbers,
pseudoperfect numbers,
primitive abundant numbers

Article copyright:
© Copyright 1974
American Mathematical Society