The independence and clique cover numbers of the squarefree graph

Abstract

We determine the largest subset $A\subseteq \{1,\dots ,n\}$ such that for all $a,b\in A$, the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the complement of the odd squarefree numbers. This resolves a problem of Paul Erdős and András Sárközy from 1992.

13 pages, 3 figures; v2 has only minor changes