It seems that as $n$ increases, the ratio $$\frac{\varphi(2^n-1)}{2^n-1}$$ takes on values reasonably often in the interval $(.3,.4)$.

Is there anything known about $$\lim \inf_{n \rightarrow \infty}n \frac{\varphi(2^n-1)}{2^n-1}?$$