On the number of divisors of Mersenne numbers

Vjekoslav Kovač, Florian Luca

Denote $f(n):={\sum }_{1\le k\le n}\ddot{I}„(2^k-1)$, where $\ddot{I}„$ is the number of divisors function. Motivated by a question of Paul Erdős, we show that the sequence of ratios $f(2n)/f(n)$…