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Media type:
E-Article
Title:
Issues in Nonlinear Hyperperfect Numbers
Contributor:
Minoli, Daniel
imprint:
American Mathematical Society, 1980
Published in:Mathematics of Computation
Language:
English
ISSN:
0025-5718;
1088-6842
Origination:
Footnote:
Description:
<p>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 $p_2 = 2^{\alpha_1^{+1}} - 1$.</p>