On the composition of a certain arithmetic function
type: Item
instance of: scholarly article
title: On the composition of a certain arithmetic function
zbMATH Open document ID: 1252.11004
author: Florian Luca
author: József Sándor
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2010-01-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1261157809
review text: The main subject of the paper under review is studying the arithmetic function \(S:\mathbb{N}\to\mathbb{N}\) defined by \(S(n)=\min\{m: n|m!\}\). The authors start their work by reviewing and obtaining some properties of \(S(n)\), and then they obtain various inequalities involving the function \(S(f(n))\) for some arithmetic functions \(f\) including the Euler function and the sum of divisors function. They also investigate the values of \(S(F_n)\) and \(S(L_n)\), where \(F_n\) and \(L_n\) are the \(n\)th Fibonacci and Lucas numbers, respectively. Finally, they obtain several limit relations involving \(S(n)\) and its various composites with some arithmetic functions.
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 5654318
zbMATH Keywords: Arithmetic functions connected with factorials
zbMATH Keywords: Fibonacci numbers
zbMATH Keywords: Lucas numbers
MaRDI profile type: Publication
OpenAlex ID: W2002827730
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DOI: 10.7169/FACM/1261157809
description: scientific article; zbMATH DE number 5654318