| 奇完全数的判定及素因数个数的估算 |
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| 引用本文： | 李锡初. 奇完全数的判定及素因数个数的估算[J]. 广西师范学院学报(自然科学版), 2003, 20(4): 50-52 |
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| 作者姓名： | 李锡初 |
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| 作者单位： | 广西图书馆,广西 南宁 530022 |
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| 摘 要： | 该文给出正整数不是奇完全数的判定定理,并据之推出,若Nk=Pa11Pa22…Pakk是奇完全数,则其素因数的个数k1)当pi＞qi时,k＞s1.2)当pi=qi时,s2＜k＜s1+1;当pi≥qi时,k＞s2.3)当pi＜qi时,k＜s2+1.其中,s1由
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| 关 键 词： | 奇完全数 判定 素因数 |
| 文章编号： | 1002-8743(2003)04-0050-03 |
| 修稿时间： | 2003-09-19 |
Decision of Odd Perfect Number and Number of Prime Factors of Odd Perfect Numbers |
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| LI Xi-chu. Decision of Odd Perfect Number and Number of Prime Factors of Odd Perfect Numbers[J]. Journal of Guangxi Teachers Education University:Natural Science Edition, 2003, 20(4): 50-52 |
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| Authors: | LI Xi-chu |
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| Abstract: | This article puts forward a decision theorem that if a positive integer N k=p a 1 1p a 2 2...p a k k is an odd perfect number, then k (number of prime factors of N k) satisfies: 1)p i>q i,k>s 1; 2)p i=q i,s 21 2q 1q 2...q s 1 q s 1+1 (1+q 1)(1+q 2)...(1+q s 1 )(1+q s 1+1 )<1. s 2 is determined by 2(q 1-1)(q 2-1)...(q s 2 -1)q 1q 2...q s 2 >12(q 1-1)(q 2-1)...(q s 2 -1)(q s 2+1 -1)q 1q 2...q s 2 q s 2+1 <1. q 1,q 2,...,q i are adjacent prime numbers. |
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| Keywords: | odd perfect number decision prime factors of odd perfect number |
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