erdos_12.parts.i

Let $A$ be an infinite set such that there are no distinct $a,b,c \in A$ such that $a \mid (b+c)$ and $b,c > a$. Is there such an $A$ with $\liminf \frac{|A \cap \{1, \dotsc, N\}|}{N^{1/2}} > 0$ ?

theorem erdos_12.parts.i : answer(sorry) ↔ ∃ (A : Set ℕ), IsGood A ∧
    (0 : ℝ) < Filter.atTop.liminf
      (fun N => (A.interIcc 1 N).ncard / (N : ℝ).sqrt)

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