erdos_12.variants.schoen

Let $A$ be a set of natural numbers with the property that there are no distinct $a,b,c \in A$ such that $a \mid (b+c)$ and $b,c > a$. If all elements in $A$ are pairwise coprime then \[\lvert A\cap\{1,\ldots,N\}\rvert \ll N^{2/3}\]

theorem erdos_12.variants.schoen (A : Set ℕ) (hA : IsGood A) (hA' : A.Pairwise Nat.Coprime) :
    (fun N ↦ ((A.interIcc 1 N).ncard : ℝ)) =O[atTop] (fun N ↦ (N : ℝ) ^ (2 / 3 : ℝ))

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