Issues in nonlinear hyperperfect numbers
Author:
Daniel Minoli
Journal:
Math. Comp. 34 (1980), 639645
MSC:
Primary 10A20
DOI:
https://doi.org/10.1090/S00255718198005592069
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 2HP 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 (1HP) 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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Article copyright:
© Copyright 1980
American Mathematical Society