Functiones et Approximatio Commentarii Mathematici

On the composition of a certain arithmetic function

Florian Luca and József Sándor

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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

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

First available in Project Euclid: 18 December 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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