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BOUNDS FOR ODD k-PERFECT NUMBERS

Part of: Elementary number theory

Published online by Cambridge University Press:  21 July 2011

SHI-CHAO CHEN  and
HAO LUO
SHI-CHAO CHEN*
Affiliation:
Institute of Applied Mathematics, School of Mathematics and Information Science, Henan University, Kaifeng 475004, PR China (email: schen@henu.edu.cn)
HAO LUO
Affiliation:
Institute of Applied Mathematics, School of Mathematics and Information Science, Henan University, Kaifeng 475004, PR China (email: luohao200681@126.com)
*
✉For correspondence; e-mail: schen@henu.edu.cn
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Abstract

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Let k≥2 be an integer. A natural number n is called k-perfect if σ(n)=kn. For any integer r≥1, we prove that the number of odd k-perfect numbers with at most r distinct prime factors is bounded by (k−1)4r3.

Keywords

odd perfect numbermultiperfect number

MSC classification

Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 475 - 480
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Supported by the Natural Science Foundation of China (Grant 11026080) and the Natural Science Foundation of Education Department of Henan Province (Grant 2009A110001).

References

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