Geodesic
On square values of the product of the Euler totient and sum of divisors functions
Kevin Broughan1 ; Kevin Ford2 ; Florian Luca3
1 Department of Mathematics University of Waikato Private Bag 3105, Hamilton, New Zealand
2 Department of Mathematics The University of Illinois at Urbana-Champaign Urbana 1409 West Green St. Champaign, IL 61801, U.S.A.
3 Fundación Marcos Moshinsky Instituto de Ciencias Nucleares UNAM Circuito Exterior, C.U., Apdo. Postal 70-543 México, D.F. 04510, Mexico
Colloquium Mathematicum, Tome 130 (2013) no. 1, pp. 127-137.

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

If $n$ is a positive integer such that $\phi (n)\sigma (n)=m^2$ for some positive integer $m$, then $m\le n$. We put $m=n-a$ and we study the positive integers $a$ arising in this way.
DOI : 10.4064/cm130-1-11
Keywords: positive integer phi sigma positive integer put n a study positive integers arising

Kevin Broughan 1 ; Kevin Ford 2 ; Florian Luca 3

1 Department of Mathematics University of Waikato Private Bag 3105, Hamilton, New Zealand
2 Department of Mathematics The University of Illinois at Urbana-Champaign Urbana 1409 West Green St. Champaign, IL 61801, U.S.A.
3 Fundación Marcos Moshinsky Instituto de Ciencias Nucleares UNAM Circuito Exterior, C.U., Apdo. Postal 70-543 México, D.F. 04510, Mexico 
@article{10_4064_cm130_1_11,
     author = {Kevin Broughan and Kevin Ford and Florian Luca},
     title = {On square values of the product of the {Euler} totient and sum of divisors functions},
     journal = {Colloquium Mathematicum},
     pages = {127--137},
     publisher = {mathdoc},
     volume = {130},
     number = {1},
     year = {2013},
     doi = {10.4064/cm130-1-11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm130-1-11/}
}
TY  - JOUR
AU  - Kevin Broughan
AU  - Kevin Ford
AU  - Florian Luca
TI  - On square values of the product of the Euler totient and sum of divisors functions
JO  - Colloquium Mathematicum
PY  - 2013
SP  - 127
EP  - 137
VL  - 130
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm130-1-11/
DO  - 10.4064/cm130-1-11
LA  - en
ID  - 10_4064_cm130_1_11
ER  - 
%0 Journal Article
%A Kevin Broughan
%A Kevin Ford
%A Florian Luca
%T On square values of the product of the Euler totient and sum of divisors functions
%J Colloquium Mathematicum
%D 2013
%P 127-137
%V 130
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm130-1-11/
%R 10.4064/cm130-1-11
%G en
%F 10_4064_cm130_1_11
Kevin Broughan; Kevin Ford; Florian Luca. On square values of the product of the Euler totient and sum of divisors functions. Colloquium Mathematicum, Tome 130 (2013) no. 1, pp. 127-137. doi : 10.4064/cm130-1-11. http://geodesic.mathdoc.fr/articles/10.4064/cm130-1-11/

Cité par Sources :