1Département de mathématiques Université Laval Québec G1V 0A6, Canada 2Computer Algebra Department Eötvös Lorand University Pázmány Péter sétány 1/C 1117 Budapest, Hungary
Colloquium Mathematicum, Tome 147 (2017) no. 2, pp. 247-255
Let $\gamma(n)$ stand for the product of the prime factors of $n$. The index of composition $\lambda(n)$ of an integer $n\ge 2$ is defined as $\lambda(n)=\log n / \!\log \gamma(n)$ with $\lambda(1)=1$.
Given an arbitrary integer $k\ge 0$ and letting $\sigma_k(n)$ be the $k$-fold iterate of the sum of divisors function, we show that, given any real number $\varepsilon \gt 0$, $\lambda(\sigma_k(n)) \lt 1+\varepsilon$ for almost all positive integers $n$.
Keywords:
gamma stand product prime factors index composition lambda integer defined lambda log log gamma lambda given arbitrary integer letting sigma k fold iterate sum divisors function given real number varepsilon lambda sigma varepsilon almost positive integers
Affiliations des auteurs :
Jean-Marie De Koninck
1
;
Imre Kátai
2
1
Département de mathématiques Université Laval Québec G1V 0A6, Canada
2
Computer Algebra Department Eötvös Lorand University Pázmány Péter sétány 1/C 1117 Budapest, Hungary
@article{10_4064_cm6880_6_2016,
author = {Jean-Marie De Koninck and Imre K\'atai},
title = {On the $k$-fold iterate of the sum of divisors function},
journal = {Colloquium Mathematicum},
pages = {247--255},
year = {2017},
volume = {147},
number = {2},
doi = {10.4064/cm6880-6-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6880-6-2016/}
}
TY - JOUR
AU - Jean-Marie De Koninck
AU - Imre Kátai
TI - On the $k$-fold iterate of the sum of divisors function
JO - Colloquium Mathematicum
PY - 2017
SP - 247
EP - 255
VL - 147
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm6880-6-2016/
DO - 10.4064/cm6880-6-2016
LA - en
ID - 10_4064_cm6880_6_2016
ER -
%0 Journal Article
%A Jean-Marie De Koninck
%A Imre Kátai
%T On the $k$-fold iterate of the sum of divisors function
%J Colloquium Mathematicum
%D 2017
%P 247-255
%V 147
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm6880-6-2016/
%R 10.4064/cm6880-6-2016
%G en
%F 10_4064_cm6880_6_2016
Jean-Marie De Koninck; Imre Kátai. On the $k$-fold iterate of the sum of divisors function. Colloquium Mathematicum, Tome 147 (2017) no. 2, pp. 247-255. doi: 10.4064/cm6880-6-2016
