Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers

Gryszka, Karol

doi:10.2478/amsil-2023-0013

.blurhash-client-img { display: none !important; }

Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers

Annales Mathematicae Silesianae

Volume 37 (2023): Issue 2 (September 2023)

By: Karol Gryszka

Open Access

|Jul 2023

Abstract

In this article, we derive a great number of identities involving the ω function counting distinct prime divisors of a given number n. These identities also include Pochhammer symbols, Fibonacci and Lucas numbers and many more.

References

R. Battaloglu and Y. Simsek, On new formulas of Fibonacci and Lucas numbers involving golden ratio associated with atomic structure in chemistry, Symmetry 13 (2021), no. 8, Paper No. 1334, 10 pp.
Search in Google Scholar Back to article
K. Gryszka, Binomial formulas via divisors of numbers, Notes Number Theory Discrete Math. 27 (2021), no. 4, 122–128.
Search in Google Scholar Back to article
G.H. Hardy and E.M. Wright,An Introduction to the Theory of Numbers, sixth edition, Oxford University Press, Oxford, 2008.
Search in Google Scholar Back to article
R. Jakimczuk, On the function !(n), Int. Math. Forum 13 (2018), no. 3, 107–116.
Search in Google Scholar Back to article
S. Lang, Algebra, revised third edition, Graduate Texts in Mathematics, 211, Springer-Verlag, New York, 2002.
Search in Google Scholar Back to article
G. Liu, An identity involving the Lucas numbers and Stirling numbers, Fibonacci Quart. 46/47 (2008/2009), no. 2, 136–139.
Search in Google Scholar Back to article
N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, 2021. https://oeis.org/A105278
Search in Google Scholar Back to article
M.V. Vassilev-Missana, New form of the Newton’s binomial theorem, Notes Number Theory Discrete Math. 25 (2019), no. 1, 48–49.
Search in Google Scholar Back to article
T. Wakhare, Sums involving the number of distinct prime factors function, Rose-Hulman Undergrad. Math. J. 19 (2018), no. 1, Art. 8, 13 pp.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/amsil-2023-0013 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 266 - 293

Submitted on: Jan 3, 2023

Accepted on: Jul 13, 2023

Published on: Jul 26, 2023

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

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

divisor,

multiplicative function,

symmetric polynomial,

Related subjects:

© 2023 Karol Gryszka, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Previous article Volume 37 (2023): Issue 2 (September 2023)Next article