Erdős problem 269

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

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

269.lean

Retained formal statement1 of 3

This theorem addresses the case where the set of primes $P$ is infinite. In this case the sum is irrational.

FormalConjectures/ErdosProblems/269.leanErdos269.erdos_269.variants.infinite1 lineExact file

1∀ (P : Set ℕ), (∀ p ∈ P, Nat.Prime p) → P.Infinite → Irrational (Erdos269.series P)

SolvedStatement only, no proof