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.
Publié le : 2009-12-15
Classification:
Arithmetic functions connected with factorials,
maximal orders of compositions of arithmetic functions,
the largest prime factor of an integer,
Fibonacci numbers,
congruences,
11A25,
11B39,
11N37,
11N56
@article{1261157809,
author = {Luca, Florian and S\'andor, J\'ozsef},
title = {On the composition of a certain arithmetic function},
journal = {Funct. Approx. Comment. Math.},
volume = {40},
number = {1},
year = {2009},
pages = { 185-209},
language = {en},
url = {http://dml.mathdoc.fr/item/1261157809}
}
Luca, Florian; Sándor, József. On the composition of a certain arithmetic function. Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, pp. 185-209. http://gdmltest.u-ga.fr/item/1261157809/