erdos_126

Let $f(n)$ be maximal such that if $A\subseteq\mathbb{N}$ has $|A| = n$ then $\prod_{a\neq b\in A}(a + b)$ has at least $f(n)$ distinct prime factors. Is it true that $\frac{f(n)}{\log n} \to\infty$?

theorem erdos_126 : answer(sorry) ↔ ∀ (f : ℕ → ℕ), IsMaximalAddFactorsCard f →
    Tendsto (fun n => f n / Real.log n) atTop atTop

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