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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On weird and pseudoperfect numbers
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by S. J. Benkoski and P. Erdős PDF
Math. Comp. 28 (1974), 617-623 Request permission


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.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 617-623
  • MSC: Primary 10A40
  • DOI:
  • MathSciNet review: 0347726