Erdős Problem 856

### What is the conjecture

https://www.erdosproblems.com/856

Let $k\geq 3$ and $f_k(N)$ be the maximum value of $\sum_{n\in A}\frac{1}{n}$, where $A$ ranges over all subsets of $\\{1,\ldots,N\\}$ which contain no subset of size $k$ with the same pairwise least common multiple.

Estimate $f_k(N)$.

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