erdos_890.parts.b

Is it true that $\limsup_{n\to \infty}\left(\sum_{0\leq i < k}\omega(n+i)\right) \frac{\log\log n}{\log n}=1?$

theorem erdos_890.parts.b :
    answer(sorry) ↔ ∀ k ≥ 1, limsup (fun n ↦ (∑ i ∈ range k, (ω (n + i) : EReal)) *
      (log (log n) / log n)) atTop = 1

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