关于无平方因子数的倒数和问题

On the sums of reciprocals of square-free numbers

如果一个正整数不能被大于1的平方数整除,则称这个正整数为无平方因子数.对于无平方因子数的分布,表示整数为无平方因子数的和等其他问题,现已有了很多深刻的研究.设(a,s)=1.论文研究了,并且给出了它们的渐进公式.

A positive integer q is called square-free number if it is the product of distinct prime number or q = 1. For the distribution of square-free numbers, representing integers by a sum of square free numbers some other related problems have been widely and deeply investigated. Let x be a positive real number and let （ a,s ） =1 In this paper, we investigated 1/n,n≤x,∑n无平方,n=a（s）lnn/n与1〈n〈x,∏n无平方,n=a（s）（1-1/n）,and gave them asympotic formulars.