Erdős Problem 858

### What is the conjecture

https://www.erdosproblems.com/858

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
$$\frac{1}{\log N}\sum_{n\in A}\frac{1}{n}.$$

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else