{"docId":10527,"paperId":10527,"url":"https:\/\/cm.episciences.org\/10527","doi":"10.46298\/cm.10527","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":612,"name":"Volume 30 (2022), Issue 1"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2212.09477","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/2212.09477v2","dateSubmitted":"2022-12-21 16:37:39","dateAccepted":"2022-12-21 22:18:41","datePublished":"2022-12-26 12:05:09","titles":["On square-free numbers generated from given sets of primes"],"authors":["Roman, G."],"abstracts":["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 $\\mathcal{P}$."],"keywords":["Mathematics - Number Theory"]}