Erdős Problem 131: Maximal sets with non-dividing property

### What is the conjecture

https://www.erdosproblems.com/131

Let $F(N)$ be the maximal size of $A\subseteq\{1,\ldots,N\}$ such that no $a\in A$ divides the sum of any distinct elements of $A\backslash\{a\}$. Estimate $F(N)$ - is it true that
$F(N) > N^{1/2-o(1)}?$

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