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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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Spoof odd perfect numbers
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by Samuel J. Dittmer PDF
Math. Comp. 83 (2014), 2575-2582 Request permission

Abstract:

In 1638, Descartes showed that $3^2 \cdot 7^2 \cdot 11^2 \cdot 13^2 \cdot 22021^1$ would be an odd perfect number if $22021$ were prime. We give a formal definition for such “spoof” odd perfect numbers, and construct an algorithm to find all such integers with a given number of distinct quasi-prime factors. We show that Descartes’ example is the only spoof with less than seven such factors.
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Additional Information
  • Samuel J. Dittmer
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • Email: samuel.dittmer@gmail.com
  • Received by editor(s): June 19, 2012
  • Received by editor(s) in revised form: January 16, 2013
  • Published electronically: October 25, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2575-2582
  • MSC (2010): Primary 11A25; Secondary 11A05, 11A67, 11D72, 11N80
  • DOI: https://doi.org/10.1090/S0025-5718-2013-02793-7
  • MathSciNet review: 3223347