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

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.