Erdős Problem 879

### What is the conjecture

https://www.erdosproblems.com/879

Call a set $S\subseteq \\{1,\ldots,n\\}$ admissible if $(a,b)=1$ for all $a\neq b\in S$. Let
$$G(n) = \max_{S\subseteq \\{1,\ldots,n\\}} \sum_{a\in S}a$$
and
$$H(n)=\sum_{pH(n)-n^{1+o(1)}?$$
Is it true that, for every $k\geq 2$, if $n$ is sufficiently large then the admissible set which maximises $G(n)$ contains at least one integer with at least $k$ prime factors?

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