Erdős Problem 646

Let $p_1,\ldots,p_k$ be distinct primes. Are there infinitely many $n$ such that $n!$ is divisible by an even power of each of the $p_i$?

The answer is yes, proved by Berend [Be97], who further proved that the sequence of such $n$ has bounded gaps (where the bound depends on the initial set of primes).