Erdős Problem #1049

declared status 'open'. Formalized: yes. 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 $n$? Current best: Erd\H{o}s [Er48] proved that this is true if $t\geq 2$ is an integer. Prize: no. Tags: irrationality.

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