| 一类奇完全数的相异素因子个数 |
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| 作者姓名： | 张四保 邓勇 |
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| 作者单位： | 喀什师范学院数学系, 喀什 844007 |
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| 基金项目： | Supported by the High Education Item of Xinjiang Uighur Autonomous Region (XJEDU2008I31 ); the Science Foundation of Kashgar Teacher College (092307) |
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| 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.
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| 关 键 词： | 完全数 奇完全数 约数和函数 |
| 收稿时间： | 2010-06-24 |
| 修稿时间： | 2010-10-15 |
Brief Report Number ω(n) of distinct prime factors for a kind of odd perfect number |
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| Authors: | ZHANG Si-Bao DENG Yong |
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| Institution: | Department of Mathematics, Kashgar Teachers College, Kashgar 844007, China |
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| 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. |
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| Keywords: | perfect number odd perfect number the sum of factors |
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