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ADDITION TO ‘AN UPPER BOUND FOR THE NUMBER OF ODD MULTIPERFECT NUMBERS’

Part of: Elementary number theory

Published online by Cambridge University Press:  07 June 2013

PINGZHI YUAN  and
ZHONGFENG ZHANG
PINGZHI YUAN*
Affiliation:
School of Mathematics, South China Normal University, Guangzhou 510631, PR China
ZHONGFENG ZHANG
Affiliation:
School of Mathematics and Informational Science, Zhaoqing University, Zhaoqing, 526061, PR China email [email protected]
*
✉[email protected]
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Abstract

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The main result in the earlier paper (by the first author) is improved as follows. The number of odd multiperfect numbers with at most $r$ distinct prime factors is bounded by ${4}^{{r}^{2} } / {2}^{r+ 2} (r- 1)!$.

Keywords

odd perfect numbersk-perfect numbers

MSC classification

Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 5 - 7
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

McCarthy, P. J., ‘Odd perfect numbers’, Scripta Math. 23 (1957), 43–47.Google Scholar
Nielsen, P., ‘An upper bound for odd perfect numbers’, Integers 3 (2003), A14, 9 pages (electronic).Google Scholar
Pollack, P., ‘On Dickson’s theorem concerning odd perfect numbers’, Amer. Math. Monthly 118 (2011), 161–164.Google Scholar
Yuan, P., ‘An upper bound for the number of odd multiperfect numbers’, Bull. Aust. Math. Soc., to appear.Google Scholar