Affiliation:
1. Department of Mathematics, Hofstra University, Hempstead 11550, NY, USA
Abstract
For a positive integern, letP(n)denotes the largest prime divisor ofnand define the set:𝒮(x)=𝒮={n≤x:n does not divide P(n)!}. Paul Erdös has proposed that|S|=o(x)asx→∞, where|S|is the number ofn∈S. This was proved by Ilias Kastanas. In this paper we will show the stronger result that|S|=O(xe−1/4logx).
Subject
Mathematics (miscellaneous)
Cited by
2 articles.
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1. Polynomial analogue of the Smarandache function;Journal of Number Theory;2020-12
2. A Divisibility Theorem For Factorials;Journal of Mathematical Analysis and Applications;2000-09