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NOTE ON ODD MULTIPERFECT NUMBERS

Part of: Combinatorics Elementary number theory

Published online by Cambridge University Press:  17 September 2012

LI-XIA DAI ,
HAO PAN  and
CUI-E TANG
LI-XIA DAI
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China (email: lilidainjnu@163.com)
HAO PAN*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, PR China (email: haopan79@yahoo.com.cn)
CUI-E TANG
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China (email: tangcuie2008@126.com)
*
✉For correspondence; e-mail: haopan79@yahoo.com.cn
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Abstract

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For $k\geq 2$ and $r\geq 1$, we prove that the number of odd $k$-perfect numbers with $r$ distinct prime factors is at most $4^{r^2}(k-1)^{2r^2+3}$.

Keywords

multiperfect numbermultiplicative partition function

MSC classification

Secondary: 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors 05A17: Partitions of integers

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 3 , June 2013 , pp. 448 - 451
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

References

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