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].

A general version asks, for a fixed $r \in \mathbb{N}$, if a set $A \subseteq \{1, ..., N\}$ has no $a \in A$ and $b_1, ..., b_r \in A$ such that $a | (b_1 + ... + b_r)$ and $a < \min(b_1, ..., b_r)$, then is it true that $|A| \le N/(r+1) + O(1)$?