## Functiones et Approximatio Commentarii Mathematici

### On the composition of a certain arithmetic function

#### 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

https://projecteuclid.org/euclid.facm/1261157809

Digital Object Identifier
doi:10.7169/facm/1261157809

Mathematical Reviews number (MathSciNet)
MR2590333

Zentralblatt MATH identifier
1252.11004

#### 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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