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›› 2011, Vol. 28 ›› Issue (4): 548-550.DOI: 10.7523/j.issn.2095-6134.2011.4.016

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Brief Report Number ω(n) of distinct prime factors for a kind of odd perfect number

ZHANG Si-Bao, DENG Yong   

  1. Department of Mathematics, Kashgar Teachers College, Kashgar 844007, China
  • Received:2010-06-24 Revised:2010-10-15 Online:2011-07-15
  • Supported by:

    Supported by the High Education Item of Xinjiang Uighur Autonomous Region (XJEDU2008I31 ); the Science Foundation of Kashgar Teacher College (092307) 

Abstract:

The existence of odd perfect numbers is a well-known open problem in number theory. We prove that if n is an odd perfect number which is relatively prime to 3, then ω(n)≥16, where ω(n) is the number of distinct prime factors of n.

Key words: perfect number, odd perfect number, the sum of factors

CLC Number: