收稿日期: 2010-06-24
修回日期: 2010-10-15
网络出版日期: 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
Received date: 2010-06-24
Revised date: 2010-10-15
Online 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)
张四保 , 邓勇 . 一类奇完全数的相异素因子个数[J]. 中国科学院大学学报, 2011 , 28(4) : 548 -550 . DOI: 10.7523/j.issn.2095-6134.2011.4.016
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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