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 statement2 of 3

Show that $\sum_{n} \frac{d(n)}{2^n}$ is irrational.

[Er48] Erdős, P., _On arithmetical properties of Lambert series_. J. Indian Math. Soc. (N.S.) (1948), 63-66.

FormalConjectures/ErdosProblems/257.leanErdos257.erdos_257.variants.tsum_top1 lineExact file

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

SolvedStatement only, no proof