Erdős Problem 784

### What is the conjecture

https://www.erdosproblems.com/784

Let $C>0$ be some constant and $n$ be large. If $A\subseteq\\{1,\ldots,n\\}$ has $\sum_{n\in A}\frac{1}{n}\leq C$ then is there some $c$ (which may depend on $C$) such that
$$\\{ m\leq n : a\nmid m\textrm{ for all }a\in A\\}$$
has size $\geq n/(\log n)^{c}$?

Status: solved

### 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

Read the linked Erdős Problems 784 statement and review the formalized conjectures in this repository before choosing an entry point. The work is complete when this solved conjecture has been added as a formalized Lean statement in the collection.

Written by the indexing model from the issue text.