# Mersenne number with small Carmichael function

Let $\lambda(\cdot)$ be the Carmichael function. I'm trying to understand the magnitude of the smallest values of $\lambda(2^n - 1)$, when $n$ runs over the positive integers. Precisely my question is:

Can we prove that $\lambda(2^n - 1) \ll 2^{o(n)}$ for infinitely many positive integers $n$?

• @GerhardPaseman Here jpst.it/-jHl you find all pairs $n, \; \lambda(2^n - 1)$ for $n=1,\ldots,100$ – user40023 Jun 7 '17 at 14:45