Geodesic
On the composition of the Euler function and the sum of divisors function
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
Colloquium Mathematicum, Tome 108 (2007) no. 1, pp. 31-51 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 
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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

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