International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1999 / Article

Open Access

Volume 22 |Article ID 645604 | https://doi.org/10.1155/S0161171299226555

Safwan Akbik, "On a density problem of Erdös", International Journal of Mathematics and Mathematical Sciences, vol. 22, Article ID 645604, 4 pages, 1999. https://doi.org/10.1155/S0161171299226555

On a density problem of Erdös

Received13 Apr 1998
Revised10 Jun 1998

Abstract

For a positive integer n, let P(n) denotes the largest prime divisor of n and define the set: 𝒮(x)=𝒮={nx:ndoes not divideP(n)!}. Paul Erdös has proposed that |S|=o(x) as x, where |S| is the number of nS. This was proved by Ilias Kastanas. In this paper we will show the stronger result that |S|=O(xe1/4logx).

Copyright © 1999 Hindawi Publishing Corporation. 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.


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