OPEN
This is open, and cannot be resolved with a finite computation.
Let $t>1$ be a rational number. Is\[\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n}\]irrational, where $\tau(n)$ counts the divisors of $n$?
A conjecture of Chowla. Erdős
[Er48] proved that this is true if $t\geq 2$ is an integer.
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This page was last edited 28 September 2025.
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #1049, https://www.erdosproblems.com/1049, accessed 2025-11-16
