期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2003
卷号：2003
DOI：10.1155/S016117120320418X
出版社：Hindawi Publishing Corporation
摘要：For each integer n≥2, let P(n) denote its largest prime factor. Let S:={n≥2:n does not divide P(n)!} and S(x):=#{n≤x:n∈S}. Erdős (1991) conjectured that S is a set of zero density. This was proved by Kastanas (1994) who established that S(x)=O(x/logx). Recently, Akbik (1999) proved that S(x)=O(x exp{−(1/4)logx}). In this paper, we show that S(x)=x exp{−(2
