一类奇完全数的相异素因子个数

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(n)≥16,其中ω(n)表示为奇完全数n相异素因子的个数.%The existence of odd perfect numbers is a well-known open problem in number theory.We prove that ifn 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.