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).