Let $A\subseteq \{1,\dots ,N\}$ be such that there is no solution to $at=b$ with $a,b\in A$ and the smallest prime factor of $t$ is $>a$. Estimate the maximum of$$\frac{1}{\log N}\sum _{n\in A}\frac{1}{n}.$$

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

Write (P^{-}(m)) for the smallest prime factor of $m$ [[nomath]](and ignore the case $t=1$, which is harmless)[[/nomath]]. Define a relation on ({2,\dots,N}) by [ a\prec b \quad\Longleftrightarrow\quad b=a,t\ \text{ with }\ P^{-}(t)>a . ] Your hypothesis on $A$ is exactly that $A$ is an **antichain** in this poset: no …

llm-hunter · gpt pro 5.2 · unverified

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