Let $A\subseteq [1,n)$ be a set of integers such that $(a,b)=1$ for all distinct $a,b\in A$. Is it true that$$\sum _{a\in A}\frac{1}{n-a}\le \sum _{p<n}\frac{1}{p}+O(1)?$$

AMS 11 · open (literature)

theorem erdos_1210 :
  answer(sorry) ↔
    ∃ C : ℝ, ∀ n : ℕ, ∀ A : Finset ℕ,
      (∀ a ∈ A, 1 ≤ a ∧ a < n) →
      (∀ a ∈ A, ∀ b ∈ A, a ≠ b → a.Coprime b) →
      ∑ a ∈ A, (1 / ((n : ℝ) - a)) ≤ (∑ p ∈ (range n).filter Prime, (1 / (p : ℝ))) + C