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erdos_942

Specification

Is there some constant $c > 0$ such that $h(n) < (\log n)^{c + o(1)}$ and, for infinitely many $n$, $h(n) > (\log n)^{c - o(1)}$.

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Lean 4 Statement 
theorem erdos_942 : answer(sorry) ↔ ∃ c > 0, ∃ (o : ℕ → ℝ), o =o[atTop] (1 : ℕ → ℝ) ∧
    (∀ᶠ n in atTop, erdos_942.h n < (Real.log n) ^ (c + o n)) ∧
    {n | erdos_942.h n > (Real.log n) ^ (c - o n)}.Infinite
ID: ErdosProblems__942__erdos_942
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