Problem 858

Erdős Problem #858: declared status 'solved'. Formalized: no. Let $A\subseteq \{1,\ldots,N\}$ be such that there is no solution to $at=b$ with $a,b\in A$ and the smallest prime factor of $t$ is $>a$. Estimate the maximum of$$\frac{1}{\log N}\sum_{n\in A}\frac{1}{n}.$$ Prize: no. Tags: number theory, primitive sets.