Some general theorems about a class of sets of numbers

Rafael Jakimczuk

Published: 2023-12-13

Vol. 38 No. 2 (2024)

Some general theorems about a class of sets of numbers

Rafael Jakimczuk

Abstract

We prove a theorem which unifies some formulas, for example the counting function of some sets of numbers including all positive integers, h-free numbers, h-full numbers, etc. We also establish a conjecture and give some examples where the conjecture holds.

Keywords:

sets of numbers , counting function , general theorems , least prime factor

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Jakimczuk, R. (2023). Some general theorems about a class of sets of numbers. Annales Mathematicae Silesianae, 38(2), 314–335. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/16499

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References

G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, Oxford, at the Clarendon Press, 1960.
Google Scholar

A. Ivić, The Riemann Zeta-Function, Dover Publications, Inc., Mineola, NY, 2003.
Google Scholar

A. Ivić and P. Shiu, The distribution of powerful integers, Illinois J. Math. 26 (1982), no. 4, 576–590.
Google Scholar

R. Jakimczuk, The kernel of powerful numbers, Int. Math. Forum 12 (2017), no. 15, 721–730.
Google Scholar

R. Jakimczuk and M. Lalín, Sums of ω(n) and Ω(n) over the k-free parts and k-full parts of some particular sequences, Integers 22 (2022), Paper No. A113, 22 pp.
Google Scholar

I. Niven, Averages of exponents in factoring integers, Proc. Amer. Math. Soc. 22 (1969), 356–360.
Google Scholar

Vol. 38 No. 2 (2024)
Published: 2024-07-23

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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