奇完全数素因子指数的下界和相异素因子个数  

The Lower Bound on the Index of Odd Perfect Prime Factors and the Number of Different Prime Factors

作　　者：李妍玲 陈慧娇 吴晓玲 谭嘉欣 LI Yan-ling;CHEN Hui-jiao;WU Xiao-ling;TAN Jia-xin(College of Mathematics and Statistics,Hanshan Normal University,Chaozhou,Guangdong,521041)

机构地区：[1]韩山师范学院数学与统计学院,广东潮州521041

出　　处：《韩山师范学院学报》2022年第3期11-15,共5页Journal of Hanshan Normal University

基　　金：2020年大学生创新创业训练计划项目(项目编号:202021).

摘　　要：奇完全数的存在性问题是一个著名的数论难题.文章证明了不被3和5同时整除的奇完全数相异素因子的个数不少于221个的结论的同时,也推导出奇完全数每个素因子的指数大于等于k-1,其中k为该奇完全数相异素因子的个数.The existence of odd perfect numbers is a famous problem in number theory.In this study,it is proved that there are no less than 221 odd perfect prime factors which are not divisible by 3 and 5 at the same time,and it is deduced that the index of each odd perfect prime factor is greater than or equal to k-1,where k is the number of odd perfect prime factors.

关 键 词：奇完全数 素因子 指数的下界 相异素因子的个数 

分 类 号：O156[理学—数学]