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Erdős problem 269

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Let PP be a finite set of primes with ∣P∣≥2|P| \ge 2 and let {a1<a2<… }\{a_1 < a_2 < \dots\} be the set of positive integers whose prime factors are all in PP. Is the sum ∑n=1∞1[a1,…,an] \sum_{n=1}^\infty \frac{1}{[a_1,\ldots,a_n]} irrational?

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269.lean

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Let PP be a finite set of primes with ∣P∣≥2|P| \ge 2 and let {a1<a2<… }\{a_1 < a_2 < \dots\} be the set of positive integers whose prime factors are all in PP. Is the sum ∑n=1∞1[a1,…,an] \sum_{n=1}^\infty \frac{1}{[a_1,\ldots,a_n]} rational?

FormalConjectures/ErdosProblems/269.leanErdos269.erdos_269.variants.rational1 lineExact file
sorry ↔ ∀ (P : Finset ℕ), (∀ p ∈ P, Nat.Prime p) → P.card ≥ 2 → ∃ q, ↑q = Erdos269.series ↑P
OpenStatement only, no proof