erdos_13

If $A \subseteq \{1, ..., N\}$ is a set with no $a, b, c \in A$ such that $a | (b+c)$ and $a < \min(b,c)$, then $|A| \le N/3 + O(1)$. This has been solved by Bedert [Be23]. [Be23] Bedert, B., _On a problem of Erdős and Sárközy about sequences with no term dividing the sum of two larger terms_. arXiv:2301.07065 (2023).

theorem erdos_13 : ∃ C : ℝ, ∀ N : ℕ, ∀ A ⊆ Icc 1 N, IsForbiddenTripleFree A →
    (A.card : ℝ) ≤ (N : ℝ) / 3 + C

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