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Erdős problem 126

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

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FormalConjectures/ErdosProblems/

126.lean

Retained formal statement1 of 3

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

FormalConjectures/ErdosProblems/126.leanErdos126.erdos_1263 linesExact file
True ↔  ∀ (f : ℕ → ℕ),    Erdos126.IsMaximalAddFactorsCard f → Filter.Tendsto (fun n => ↑(f n) / Real.log ↑n) Filter.atTop Filter.atTop
OpenStatement only, no proof

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