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Erdős problem 1210

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Let A⊆[1,n)A\subseteq [1,n) be a set of integers such that (a,b)=1(a,b)=1 for all distinct a,b∈Aa,b\in A. Is it true that ∑a∈A1n−a≤∑p<n1p+O(1)\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)?

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Retained declaration

FormalConjectures/ErdosProblems/1210.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1210.leanErdos1210.erdos_12105 linesExact file
True ↔  ∃ C,    ∀ (n : ℕ) (A : Finset ℕ),      (∀ a ∈ A, 1 ≤ a ∧ a < n) →        (∀ a ∈ A, ∀ b ∈ A, a ≠ b → a.Coprime b) → ∑ a ∈ A, 1 / (↑n - ↑a) ≤ ∑ p ∈ Finset.range n with Prime p, 1 / ↑p + C
OpenStatement only, no proof

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