一类奇完全数的一些结论

张四保

doi:10.13371/j.cnki.chin.q.j.m.2014.02.002

数学季刊 >

2014 , Vol. 29 >Issue 2: 167 - 170

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.02.002

一类奇完全数的一些结论

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Department of Mathematics, Kashi Teacher’s College

ZHANG Si-bao(1978-), male, native of Xiajiang, Jiangxi, a lecturer of Kashi Teacher's College, M.S.D., engages in number theory.

收稿日期: 2011-11-14

网络出版日期: 2020-12-01

基金资助

Supported by the Science Foundation of Kashgar Teacher’s College(112390)；

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Some Results of a Certain Odd Perfect Number

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Department of Mathematics, Kashi Teacher’s College

ZHANG Si-bao(1978-), male, native of Xiajiang, Jiangxi, a lecturer of Kashi Teacher's College, M.S.D., engages in number theory.

Received date: 2011-11-14

Online published: 2020-12-01

Supported by

Supported by the Science Foundation of Kashgar Teacher’s College(112390)；

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摘要

Define the total number of distinct prime factors of an odd perfect number n asω(n). We prove that if n is an odd perfect number which is relatively prime to 3 and 5 and7, then ω(n) ≥ 107. And using this result, we give a conclusion that the third largest prime factor of such an odd perfect number exceeds 1283.

关键词： odd perfect numbers; the total number of distinct prime factors; the third largest prime factor

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张四保 . 一类奇完全数的一些结论[J]. 数学季刊, 2014 , 29(2) : 167 -170 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.002

Abstract

Key words： odd perfect numbers; the total number of distinct prime factors; the third largest prime factor

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