erdos_920

Is it true that, for $k\geq 4$, $f_k(n) \gg \frac{n^{1-\frac{1}{k-1}}}{(\log n)^{c_k}}$ for some constant $c_k>0$?

theorem erdos_920 :
    answer(sorry) ↔ ∀ k : ℕ, k ≥ 4 → ∃ c > 0,
      (fun n ↦ f k n) ≫ (fun n ↦ (n : ℝ) ^ (1 - 1 / ((k : ℝ) - 1)) / (log n) ^ c)

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