OPEN

Are there infinitely many $n$ such that $\binom{2n}{n}$ is coprime to $105$?

Erdős, Graham, Ruzsa, and Straus [EGRS75] have shown that, for any two primes $p$ and $q$, there are infinitely many $n$ such that $\binom{2n}{n}$ is coprime to $pq$.