Problem 131

Erdős Problem #131: declared status 'open'. Formalized: no. 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 $F(N)$. In particular, is it true that$$F(N) > N^{1/2-o(1)}?$$ Prize: no. OEIS: A068063. Tags: number theory.