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中国科学院大学学报 ›› 2011, Vol. 28 ›› Issue (4): 548-550.DOI: 10.7523/j.issn.2095-6134.2011.4.016

• 简报 • 上一篇    下一篇

一类奇完全数的相异素因子个数

张四保, 邓勇   

  1. 喀什师范学院数学系, 喀什 844007
  • 收稿日期:2010-06-24 修回日期:2010-10-15 发布日期:2011-07-15
  • 基金资助:

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

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 Published: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) 

摘要:

奇完全数的存在性问题是一个著名的数论难题. 研究了不被3整除的奇完全数相异素因子个数,证明:如果n是奇完全数,则ω(t)≥16,其中ω(n)表示为奇完全数n相异素因子的个数.

关键词: 完全数, 奇完全数, 约数和函数

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

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