Erdős Problem #320

Erdős problem #320 · erdosproblems.com/320

Let $S(N)$ count the distinct values of $\sum_{n\in A} 1/n$ over $A\subseteq\{1,\dots,N\}$ . Estimate $S(N)$ .

What the AI did

GPT-5.6 Sol (prompted by Young, Zhu, and Luo) proved a matching upper bound, pinning $\log S(N)$ to order $\frac{N}{\log N}\prod_{j\ge 3}\log_j N$ .

Marked solved on erdosproblems.com via a proof claim; not formally Lean-verified.