Problem 893

Erdős Problem #893: declared status 'open'. Formalized: yes. If $\tau(n)$ counts the divisors of $n$ then let$$f(n)=\sum_{1\leq k\leq n}\tau(2^k-1).$$Does $f(2n)/f(n)$ tend to a limit? Current best: Erd\H{o}s [Er98] says that 'probably there is no simple asymptotic formula for $f(n)$ since $f(n)$ increases too fast'. Prize: no. OEIS: A046801. Tags: divisors, number theory.