Erdős–Sárközy–Szemerédi conjecture on primitive sets

For $x\ge 1$, let $[x,\infty)$ denote the integers at least $x$, and let $f(A)=\sum_{a\in A}1/(a\log a)$ for a primitive set $A$. Erdős–Sárközy–Szemerédi conjecture.

$$\lim_{x\to\infty}\sup_{\substack{A\subset[x,\infty)\\ A\ \text{primitive}}}f(A)\le 1.$$

This question was posed by Erdős, Sárközy, and Szemerédi in 1968. The source describes it as an open question related to the primitive set conjecture; no resolution is supplied.