A question of Erdős and Selfridge [ErSe67], who observe that
$\liminf_{n\to \infty}\sum_{0\leq i < k}\omega(n+i)\geq k+\pi(k)-1$ for every $k$. This follows from
Pólya's theorem that the set of $k$-smooth integers has unbounded gaps - indeed,
$n(n+1)\cdots (n+k-1)$ is divisible by all primes $\leq k$ and, provided $n$ is large, all but at
most one of $n,n+1,\ldots,n+k-1$ has a prime factor $>k$ by Pólya's theorem.
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