Erdős Problem 311

### What is the conjecture

https://www.erdosproblems.com/311

What is the minimal value of $\lvert 1-\sum_{n\in A}\frac{1}{n}\rvert$ as $A$ ranges over all subsets of $\{1,\ldots,N\}$ which contain no $S$ such that $\sum_{n\in S}\frac{1}{n}=1$? Is it $e^{-(c+o(1))N}$ for some constant $c\in (0,1)$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else