Some Observations on the Greatest Prime Factor of an Integer

Rafael Jakimczuk

doi:10.2478/amsil-2022-0018

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Some Observations on the Greatest Prime Factor of an Integer

Annales Mathematicae Silesianae

Volume 37 (2023): Issue 1 (March 2023)

By: Rafael Jakimczuk

Open Access

|Nov 2022

Abstract

We examine the multiplicity of the greatest prime factor in k-full numbers and k-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.

References

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[2] T.M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York-Heidelberg, 1976.10.1007/978-1-4757-5579-4
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[3] O. Bordellés and L. Tóth, Additive arithmetic functions meet the inclusion-exclusion principle, II, to appear in Res. Number Theory. Avaliable at arXiv: 2112.13409.
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[4] R. Jakimczuk and M. Lalín, Sums of ω(n) and Ω (n) on the k-free parts and k-full parts of some particular sequences, preprint 2022.
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[5] R. Jakimczuk and M. Lalín, The number of prime factors on average in certain integer sequences, J. Integer Seq. 25 (2022), no. 2, Art. 22.2.3, 15 pp.
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[6] R. Jakimczuk, A note on sums of greatest (least) prime factors, Int. J. Contemp. Math. Sci. 8 (2013), no. 9–12, 423–432.
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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2022-0018 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 67 - 81

Submitted on: Mar 3, 2022

Accepted on: Nov 2, 2022

Published on: Nov 23, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

greatest prime factor,

zeta function

Related subjects:

Mathematics,

General mathematics

© 2022 Rafael Jakimczuk, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 37 (2023): Issue 1 (March 2023)