• DOI:10.46298/cm.10527
• Corpus ID: 254854115

On square-free numbers generated from given sets of primes

@article{Romn2022OnSN,
  title={On square-free numbers generated from given sets of primes},
  author={G{\'a}bor Rom{\'a}n},
  journal={Communications in Mathematics},
  year={2022}
}

• G. Román
• Published 7 December 2022
• Mathematics
• Communications in Mathematics

Let $x$ be a positive real number, and $\mathcal{P} \subset [2,\lambda(x)]$
be a set of primes, where $\lambda(x) \in o(x^{1/2})$ is a monotone increasing
function. We examine $Q_{\mathcal{P}}(x)$ for different sets $\mathcal{P}$,
where $Q_{\mathcal{P}}(x)$ is the element count of the set containing those
positive square-free integers, which are smaller than-, or equal to $x$, and
which are only divisible by the elements of $\mathcal{P}$.