Quelques inégalités effectives entre des fonctions arithmétiques usuelles
Nicolas, Jean-Louis
Funct. Approx. Comment. Math., Volume 38 (2008) no. 1, p. 315-334 / Harvested from Project Euclid
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Let us denote by $\tau(n)$ and $\sigma(n)$ the number and the sum of the divisors of $n$ and by $\varphi$ Euler's function. We give effective upper bounds for $\frac{n}{\varphi(n)}$ in terms of $\varphi(n)$, and for $\frac{\sigma(n)}{n}$ in terms of $\tau(n)$.
Published online : 2008-12-15
Classification:  Euler's function,  sum of divisors function,  champion numbers,  highly composite numbers,  11N56 
@article{1229696578,
     author = {Nicolas, Jean-Louis},
     title = {Quelques in\'egalit\'es effectives entre des fonctions arithm\'etiques usuelles},
     journal = {Funct. Approx. Comment. Math.},
     volume = {38},
     number = {1},
     year = {2008},
     pages = { 315-334},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/1229696578}
}

Nicolas, Jean-Louis. Quelques inégalités effectives entre des fonctions arithmétiques usuelles. Funct. Approx. Comment. Math., Volume 38 (2008) no. 1, pp.  315-334. http://gdmltest.u-ga.fr/item/1229696578/