On some functions involving the lcm and gcd of integer tuples

Journal article


Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B
AuthorsBagdasar, Ovidiu
Abstract

In this paper an explicit formula for the number of tuples of positive integers having the same lowest common multiple n is derived, and some of the properties of the resulting arithmetic function are analyzed. The tuples having also the same greatest common divisor are investigated, while some novel or existing integer sequences are recovered as particular cases. A formula linking the gcd and lcm for tuples of integers is also presented.

In this paper an explicit formula for the number of tuples of positive integers having
the same lowest common multiple n is derived, and some of the properties of the resulting
arithmetic function are analyzed. The tuples having also the same greatest common divisor are
investigated, while some novel or existing integer sequences are recovered as particular cases.
A formula linking the gcd and lcm for tuples of integers is also presented.

KeywordsDivisibility; Lowest common multiple; Greatest common divisor; Integer sequences
Year2014
JournalScientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics
ISSN2217-5539
Digital Object Identifier (DOI)https://doi.org/10.5937/SPSUNP1402091B
Web address (URL)http://hdl.handle.net/10545/583372
hdl:10545/583372
Publication datesJun 2014
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Deposited08 Dec 2015, 09:09
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Archived with thanks to Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics

ContributorsUniversity of Derby
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