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Erdős problem 946

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There are infinitely many nn such that τ(n)=τ(n+1)τ(n) = τ(n+1). Proved in [He84]. Here τ is the divisor counting function, which is σ 0 in mathlib.

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5 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

946.lean

Retained formal statement3 of 5

Improved lower bound in [Hi85]: Ω(x/(log⁡log⁡x)3)Ω(x / (\log \log x)^3).

FormalConjectures/ErdosProblems/946.leanErdos946.erdos_946.variants.hildebrand_lower_bound1 lineExact file
(fun x => x / Real.log (Real.log x) ^ 3) =O[Filter.atTop] Erdos946.erdos946Count
SolvedStatement only, no proof