Functiones et Approximatio Commentarii Mathematici

On the composition of a certain arithmetic function

Florian Luca and József Sándor

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Abstract

Let $S(n)$ be the function which associates for each positive integer $n$ the smallest positive integer $k$ such that $n\mid k!$. In this note, we look at various inequalities involving the composition of the function $S(n)$ with other standard arithmetic functions such as the Euler function and the sum of divisors function. We also look at 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.

Article information

Source
Funct. Approx. Comment. Math., Volume 41, Number 2 (2009), 185-209.

Dates
First available in Project Euclid: 18 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.facm/1261157809

Digital Object Identifier
doi:10.7169/facm/1261157809

Mathematical Reviews number (MathSciNet)
MR2590333

Zentralblatt MATH identifier
1252.11004

Subjects
Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations 11N37: Asymptotic results on arithmetic functions 11N56: Rate of growth of arithmetic functions

Keywords
Arithmetic functions connected with factorials maximal orders of compositions of arithmetic functions the largest prime factor of an integer Fibonacci numbers congruences

Citation

Luca, Florian; Sándor, József. On the composition of a certain arithmetic function. Funct. Approx. Comment. Math. 41 (2009), no. 2, 185--209. doi:10.7169/facm/1261157809. https://projecteuclid.org/euclid.facm/1261157809


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