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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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Issues in nonlinear hyperperfect numbers
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by Daniel Minoli PDF
Math. Comp. 34 (1980), 639-645 Request permission

Abstract:

Hyperperfect numbers (HP) are a generalization of perfect numbers and as such share remarkably similar properties. In this note we show, among other things, that if $m = p_1^{{\alpha _1}}p_2^{{\alpha _2}}$ is 2-HP then ${\alpha _2} = 1$, with ${p_1} = 3$, ${p_2} = {3^{{\alpha _1} + 1}} - 2$; this is in agreement with the structure of the perfect case (1-HP) stating that such a number is of the form $m = p_1^{{\alpha _1}}{p_2}$ with ${p_1} = 2$ and ${p_2} = {2^{{\alpha _1} + 1}} - 1$.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 639-645
  • MSC: Primary 10A20
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0559206-9
  • MathSciNet review: 559206