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BOUNDS FOR ODD k-PERFECT NUMBERS
Published online by Cambridge University Press: 21 July 2011
Abstract
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.
MSC classification
- 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).
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