Let $ϵ>0$ and $n$ be large depending on $ϵ$. Is it true that for all $n^{ϵ}<k\le n^{1-ϵ}$ the number of distinct prime divisors of $\left(\genfrac{}{}{0ex}{}{n}{k}\right)$ is$$(1+o(1))k\sum _{k<p<n}\frac{1}{p}?$$Or perhaps even when $k\ge (\log n{)}^c$?

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

Write (\omega(m)) for the number of **distinct** prime divisors of $m$.

llm-hunter · gpt pro 5.2 · unverified

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