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Erdős problem 1049

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Let t>1t>1 be a rational number. Is ∑n=1∞1tn−1=∑n=1∞τ(n)tn\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n} irrational, where τ(n)\tau(n) counts the divisors of nn?

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