Erdős Problem 169

### What is the conjecture

https://www.erdosproblems.com/169

Let $k\geq 3$ and $f(k)$ be the supremum of $\sum_{n\in A}\frac{1}{n}$ as $A$ ranges over all sets of positive integers which do not contain a $k$-term arithmetic progression. Estimate $f(k)$. Is
$$\lim_{k\to \infty}\frac{f(k)}{\log W(k)}=\infty$$
where $W(k)$ is the van der Waerden number?

Status: open

### Prerequisites needed
needs [van der Waerden number](https://en.wikipedia.org/wiki/Van_der_Waerden_number)

### 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