Erdős Problem 301

### What is the conjecture

https://www.erdosproblems.com/301

Let $f(N)$ be the size of the largest $A\subseteq \{1,\ldots,N\}$ such that there are no solutions to
$$\frac{1}{a}\neq \frac{1}{b_1}+\cdots+\frac{1}{b_k}$$
with distinct $a,b_1,\ldots,b_k\in A$? Estimate $f(N)$. In particular, is $f(N)=(\tfrac{1}{2}+o(1))N$?

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