G. Roman - On square-free numbers generated from given sets of primes

cm:10527 - Communications in Mathematics, December 26, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.10527
On square-free numbers generated from given sets of primes

Authors: G. Roman

    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 $\mathcal{P}$.


    Volume: Volume 30 (2022), Issue 1
    Published on: December 26, 2022
    Accepted on: December 21, 2022
    Submitted on: December 21, 2022
    Keywords: Mathematics - Number Theory

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