Square-full numbers with an even number of prime factors

Rafael Jakimczuk
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 21—30
DOI: 10.7546/nntdm.2020.26.1.21-30
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Authors and affiliations

Rafael Jakimczuk
División Matemática, Universidad Nacional de Luján
Buenos Aires, Argentina

Abstract

In this article, we study the functions ω(n) and Ω(n), where n is an s-full number. For example, we prove that the square-full numbers with Ω(n) even are in greater proportion than the square-full numbers with Ω(n) odd. The methods used are elementary.

Keywords

• Square-full numbers
• Arithmetical functions ω(n) and Ω(n)

2010 Mathematics Subject Classification

• 11A99
• 11B99

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