Erdős #321 (?, AMS 11). STATEMENT: Let $R(N)$ be the size of the largest $A\subseteq\{1, ..., N\}$ such that all sums $\sum_{n\in S} \frac{1}{n}$ are distinct for $S\subseteq A$. FORMAL: erdos_321: ℕ) : R N = answer(sorry); erdos_321: (fun N ↦ (R N : ℝ)) =Θ[atTop] (answer(sorry) : ℕ → ℝ); erdos_321: (fun N ↦ (R N : ℝ)) =O[atTop] (answer(sorry) : ℕ → ℝ) KNOWN/REMARKS: # Erdős Problem 321 *Reference:* erdosproblems.com/321 | Let $R(N)$ be the size of the largest $A\subseteq\{1, ..., N\}$ such that all sums $\sum_{n\in S} \frac{1}{n}$ are distinct for $S\subseteq A$. What is $R(N)$? | Formalisation note: it's possible that solution to `erdos_321` needs to be expressed asymptotically. To handle this we include `IsTheta`, `IsBigO` and `IsLittleO` variants below. Si RELATED: [] OEIS: []

id

vpr_c2eb910897b8422c

frontier

Erdős problems frontier

kind

finding.add

created

2026-06-04