Result: On primitive sets of squarefree integers

The authors provide a proof of a conjecture of Pomerance and Sárközy (a generalized version) as follows. If \(\mathbb P^{\ast}_N\) is the set of squarefree integers not exceeding \(N\), then \[ \max_{\mathcal A \in \mathbb P^{\ast}_N}\sum_{a \in \mathcal A} {1 \over a} = (1+o(1)){6 \over {\pi^2}} = {{\log N} \over {(2\pi \log \log N)^{1/2}}} \] as \(N\to \infty\). They also povide sharp estimates for \(\max_{\mathcal A \in \mathbb P^{\ast}_N}|\mathcal A|\) and some evidence for new conjectures.