Erdős problem 1049 · problems.science

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 $n$ ?

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1049.lean

Retained formal statement3 of 3

The classical Lambert series identity: $\sum_{n=1}^\infty \frac{1}{t^n - 1} = \sum_{n=1}^\infty \frac{\tau(n)}{t^n}$ , where $\tau(n)$ counts the divisors of $n$ .

FormalConjectures/ErdosProblems/1049.leanErdos1049.lambert_series_eq_num_divisor_sum1 lineExact file

1∀ (t : ℚ), ∑' (n : ℕ+), 1 / (↑t ^ ↑n - 1) = ∑' (n : ℕ+), ↑(↑n).divisors.card / ↑t ^ ↑n

TextbookStatement only, no proof

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