What is the size of the largest $A\subseteq \{1,\dots ,N\}$ such that all sums ${\sum }_{n\in S}\frac{1}{n}$ are distinct for $S\subseteq A$?

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

Let $R(N)$ denote the maximum size of a set (A\subseteq{1,\dots,N}) such that the map [ S\subseteq A \ \longmapsto\ \sum_{n\in S}\frac1n ] is injective (i.e., all these subset–reciprocal sums are distinct).

llm-hunter · gpt pro 5.2 · unverified

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