Some observations on the greatest prime factor of an integer

Rafael Jakimczuk

Published: 2022-11-23
Language: EN

Vol. 37 No. 1 (2023)

Some observations on the greatest prime factor of an integer

Rafael Jakimczuk

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.

(EN)

Keywords:

greatest prime factor , zeta function (EN)

Download files

PDF

Citation rules

Jakimczuk, R. (2022). Some observations on the greatest prime factor of an integer. Annales Mathematicae Silesianae, 37(1), 67–81. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/14910

References

K. Alladi and P. Erdos, On an additive arithmetic function, Pacific J. Math. 71 (1977), no. 2, 275–294.
Google Scholar

T.M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York-Heidelberg, 1976.
Google Scholar

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.
Google Scholar

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.
Google Scholar

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.
Google Scholar

R. Jakimczuk, A note on sums of greatest (least) prime factors, Int. J. Contemp. Math. Sci. 8 (2013), no. 9–12, 423–432.
Google Scholar

Vol. 37 No. 1 (2023)
Published: 2023-03-03

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Submit