Erdős problem 257 · problems.science

Let $A\subseteq\mathbb{N}$ be an infinite set. Is $\sum_{n\in A} \frac{1}{2^n - 1}$ irrational?

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3 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

257.lean

Retained formal statement3 of 3

Show that $\sum_{n} \frac{1}{2^n - 1} = \sum_{n} \frac{d(n)}{2^n},$ where $d(n)$ is the number of divisors of $n$ .

FormalConjectures/ErdosProblems/257.leanErdos257.erdos_257.variants.tsum_top_eq1 lineExact file

1∑' (n : ℕ), 1 / (2 ^ n - 1) = ∑' (n : ℕ), ↑n.divisors.card / 2 ^ n

TextbookStatement only, no proof