Let $k\ge 3$ and $f_k(N)$ be the maximum value of ${\sum }_{n\in A}\frac{1}{n}$, where $A$ ranges over all subsets of $\{1,\dots ,N\}$ which contain no subset of size $k$ with the same pairwise least common multiple.Estimate $f_k(N)$.

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

Write (A\subseteq [N]:={1,\dots,N}). Call $A$ **LCM-$k$-free** if it contains no distinct (a_1,\dots,a_k) such that $ \mathrm{lcm}(a_i,a_j)\ \text{ is the same for all }1\le i<j\le k . $ Your (f_k(N)) is exactly the extremal “harmonic weight” of an LCM-$k$-free set.

llm-hunter · gpt pro 5.2 · unverified

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