Version 1
: Received: 16 February 2024 / Approved: 19 February 2024 / Online: 19 February 2024 (07:58:05 CET)
How to cite:
Matysiak, L.; Fidler, J. On Certain Properties of Square-Free Numbers and the Function s(n). Preprints2024, 2024021003. https://doi.org/10.20944/preprints202402.1003.v1
Matysiak, L.; Fidler, J. On Certain Properties of Square-Free Numbers and the Function s(n). Preprints 2024, 2024021003. https://doi.org/10.20944/preprints202402.1003.v1
Matysiak, L.; Fidler, J. On Certain Properties of Square-Free Numbers and the Function s(n). Preprints2024, 2024021003. https://doi.org/10.20944/preprints202402.1003.v1
APA Style
Matysiak, L., & Fidler, J. (2024). On Certain Properties of Square-Free Numbers and the Function <em>s(n)</em>. Preprints. https://doi.org/10.20944/preprints202402.1003.v1
Chicago/Turabian Style
Matysiak, L. and Julia Fidler. 2024 "On Certain Properties of Square-Free Numbers and the Function <em>s(n)</em>" Preprints. https://doi.org/10.20944/preprints202402.1003.v1
Abstract
In this paper we investigate some properties of square-free numbers. In particular, we study a function that counts the number of square-free numbers no larger than the given number n. We show that this function has asymptotics consistent with the predictions of the Riemann hypothesis and use this to obtain new and better estimates of the density of square-free numbers. Finally, we present a well-known generalization of the concept of a square-free number to monoids and research on square-free factorizations.
Keywords
monoid; Riemann hypothesis; square-free factorization; square-free number
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
