Let $S(N)$ count the number of distinct sums of the form ${\sum }_{n\in A}\frac{1}{n}$ for $A\subseteq \{1,\dots ,N\}$. Estimate $S(N)$.

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

Write [ S(N)=|\\{\sum_{n\in A}\frac1n:;A\subseteq{1,2,\dots,N}\\}|. ] This is exactly the number of *distinct* Egyptian-fraction values whose denominators are (\le N) (each denominator used at most once), i.e. the size of the set (E_N) in the Egyptian-fraction literature. ([arXiv][1])

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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