Problem 893

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?

Source: erdosproblems.com/893

Number theory
Divisors

Wiki page

Status

Open

No claim settles this problem.

The site labels the problem OPEN. Every finite limit is ruled out by Kovač and Luca's unboundedness theorem; divergence to infinity is proved only under unproven conjectures, on their conditional page.

Problem 893

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Proof claims

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