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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Issues in nonlinear hyperperfect numbers

Author: Daniel Minoli
Journal: Math. Comp. 34 (1980), 639-645
MSC: Primary 10A20
MathSciNet review: 559206
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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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PII: S 0025-5718(1980)0559206-9
Article copyright: © Copyright 1980 American Mathematical Society

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