Geodesic
On the composition of the Euler function and the sum of divisors function
Jean-Marie De Koninck1 ; Florian Luca2
1 Département de mathématiques Université Laval Québec G1K 7P4, Canada
2 Mathematical Institute UNAM Ap. Postal 61-3 (Xangari), CP 58 089 Morelia, Michoacán, Mexico
Colloquium Mathematicum, Tome 108 (2007) no. 1, pp. 31-51

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $H(n) = {\sigma (\phi (n))/\phi (\sigma (n))}$, where $\phi (n)$ is Euler's function and $\sigma (n)$ stands for the sum of the positive divisors of $n$. We obtain the maximal and minimal orders of $H(n)$ as well as its average order, and we also prove two density theorems. In particular, we answer a question raised by Golomb.
DOI : 10.4064/cm108-1-4
Keywords: sigma phi phi sigma where phi eulers function sigma stands sum positive divisors obtain maximal minimal orders its average order prove density theorems particular answer question raised golomb

Jean-Marie De Koninck 1 ; Florian Luca 2

1 Département de mathématiques Université Laval Québec G1K 7P4, Canada
2 Mathematical Institute UNAM Ap. Postal 61-3 (Xangari), CP 58 089 Morelia, Michoacán, Mexico 
@article{10_4064_cm108_1_4,
     author = {Jean-Marie De Koninck and Florian Luca},
     title = {On the composition of
 the {Euler} function and the sum of divisors function},
     journal = {Colloquium Mathematicum},
     pages = {31--51},
     publisher = {mathdoc},
     volume = {108},
     number = {1},
     year = {2007},
     doi = {10.4064/cm108-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm108-1-4/}
}
TY  - JOUR
AU  - Jean-Marie De Koninck
AU  - Florian Luca
TI  - On the composition of
 the Euler function and the sum of divisors function
JO  - Colloquium Mathematicum
PY  - 2007
SP  - 31
EP  - 51
VL  - 108
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm108-1-4/
DO  - 10.4064/cm108-1-4
LA  - en
ID  - 10_4064_cm108_1_4
ER  - 
%0 Journal Article
%A Jean-Marie De Koninck
%A Florian Luca
%T On the composition of
 the Euler function and the sum of divisors function
%J Colloquium Mathematicum
%D 2007
%P 31-51
%V 108
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm108-1-4/
%R 10.4064/cm108-1-4
%G en
%F 10_4064_cm108_1_4
Jean-Marie De Koninck; Florian Luca. On the composition of
 the Euler function and the sum of divisors function. Colloquium Mathematicum, Tome 108 (2007) no. 1, pp. 31-51. doi: 10.4064/cm108-1-4

Cité par Sources :