Factorial divisible by Mersenn Numbers

[Masum]

Find all positive integer $n$ so that $n!$ is divisible by $2^n-1$.

[nayel]

Bang's theorem tells us that if $n\neq 1,6$ then $2^n-1$ has a primitive prime divisor $p$. If $p\le n$ then $p$ divides $2^{p-1}-1$ which is less than $2^n-1$, a contradiction. So one only needs to check $n=1,6$ of which only $n=1$ works.