Erdős problem 258

Let $a_n \to \infty$ be a sequence of non-zero natural numbers. Is $\sum_n \frac{d(n)}{(a_1 ... a_n)}$ irrational, where $d(n)$ is the number of divisors of $n$ ?

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

258.lean

Retained formal statement2 of 3

Is $\sum_n \frac{d(n)}{t^n}$ irrational, where $t ≥ 2$ is an integer.

Solution: True (proved by Erdős, see Erdős Problems website)

FormalConjectures/ErdosProblems/258.leanErdos258.erdos_258.variants.constant1 lineExact file

1True ↔ ∀ t ≥ 2, Irrational (∑' (n : ℕ), ↑(n + 1).divisors.card / ↑t ^ (n + 1))

SolvedStatement only, no proof