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 $n$?
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theorem erdos_258 : answer(sorry) ↔ ∀ (a : ℕ → ℕ), (∀ n, a n ≠ 0) →
Filter.Tendsto a Filter.atTop Filter.atTop →
Irrational (∑' (n : ℕ), ((n + 1).divisors.card / ∏ i ∈ Finset.Icc 1 n, a i))
