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Erdős problem 126

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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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The source's own material, retained exactly.

3 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

126.lean

Retained formal statement3 of 3

Erdős says that f(n)=o(nlog⁡n)f(n) = o(\frac{n}{\log n}) has never been proved.

FormalConjectures/ErdosProblems/126.leanErdos126.erdos_126.variants.isLittleO1 lineExact file
∀ (f : ℕ → ℕ), Erdos126.IsMaximalAddFactorsCard f → (fun n => ↑(f n)) =o[Filter.atTop] fun n => ↑n / Real.log ↑n
OpenStatement only, no proof