International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 655-658
doi:10.1155/S0161171299226555
On a density problem of Erdös
Department of Mathematics, Hofstra University, Hempstead 11550, NY, USA
Received 13 April 1998; Revised 10 June 1998
Copyright © 1999 Safwan Akbik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
For a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x)=𝒮={n≤x:n does not divide P(n)!}. Paul Erdös has proposed that |S|=o(x) as x→∞, where |S| is the number of n∈S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that |S|=O(xe−1/4logx).