Let $F(n)$ be the maximum possible size of a subset $A\subseteq \{1,\dots ,n\}$ such that $a\nmid bc$ whenever $a,b,c\in A$ with $a\ne b$ and $a\ne c$. Is there a constant $C$ such that$$F(n)=\pi (n)+(C+o(1))n^{2/3}(\log n{)}^{-2}?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is essentially Erdős’s “property (P_2)” extremal problem [[nomath]](sometimes phrased as the maximum size of a $2$-primitive subset of $[n]$)[[/nomath]], where one forbids a divisibility relation (a_0\mid a_1a_2) among (distinct) elements. In the standard formulation one requires (a_0,a_1,a_2) to be *all distinct*…

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.