erdos_890.parts.a

If $\omega(n)$ counts the number of distinct prime factors of $n$, then is it true that, for every $k\geq 1$, $\liminf_{n\to \infty}\sum_{0\leq i < k}\omega(n+i)\leq k+\pi(k)?$

theorem erdos_890.parts.a :
    answer(sorry) ↔ ∀ k ≥ 1, liminf (fun n ↦ (∑ i ∈ range k, (ω (n + i) : EReal))) atTop ≤ k + π k

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