A squarefreeness conjecture for Mersenne numbers

Let $p\ge 3$ be prime and set $N_p=2^p-1$. The squarefreeness conjecture. There exists $p_0$ such that, if $p>p_0$, then $N_p$ is squarefree. Squarefreeness would rule out repeated prime factors in sufficiently large prime-indexed Mersenne numbers; the source presents this as a conjecture following heuristic discussion.