I asked this question here In S.E but i don't received any resposnes for it, I would like to know if it is appropriate for M.O.

I'm always interesting for properties of the following series : $ \sum_{n=1}^{\infty }\frac{\tau(2^n-1)}{\phi(2^n-1)}$ such that: $\tau(N)$ is the number of divisors of $N$ and $\phi$ is Euler totient function, In this question i w'd be interest to know a little bit about the reciprocal of each term of the titled series at $N=2^n-1$ for every $n\geq 1$.

**Note:01** According to my calculations that i run in wolfram alpha from $n=1$ to $100$ I have got this result as shown here such that it works which letting me to ask the following question.

**My question here is:** Is ${\tau(2^n-1)}$ always divides $\phi(2^n-1)$ for every integer $n\geq 1$ and any counterexample for it?

Thank you for any help !!!