Geodesic
On the sum of the first $n$ values of the Euler function
R. Balasubramanian 1   ; Florian Luca 2   ; Dimbinaina Ralaivaosaona 3
1 The Institute of Mathematical Sciences Chennai 600 113, India
2 Mathematical Institute UNAM Juriquilla 76230 Santiago de Querétaro, México and School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg, South Africa
3 African Institute for Mathematical Sciences 6 Melrose Ave. Muizenberg, South Africa
Acta Arithmetica, Tome 163 (2014) no. 3, pp. 199-201 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\phi (n)$ be the Euler function of $n$. We put $E(n)= \sum _{m\le n} \phi (m)-(3/\pi ^2) n^2$ and give an asymptotic formula for the second moment of $E(n)$.
DOI : 10.4064/aa163-3-1
Keywords: phi euler function put sum phi asymptotic formula second moment

R. Balasubramanian  1   ; Florian Luca  2   ; Dimbinaina Ralaivaosaona  3

1 The Institute of Mathematical Sciences Chennai 600 113, India
2 Mathematical Institute UNAM Juriquilla 76230 Santiago de Querétaro, México and School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg, South Africa
3 African Institute for Mathematical Sciences 6 Melrose Ave. Muizenberg, South Africa 
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     title = {On the sum of the first $n$ values of the {Euler} function},
     journal = {Acta Arithmetica},
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R. Balasubramanian; Florian Luca; Dimbinaina Ralaivaosaona. On the sum of the first $n$ values of the Euler function. Acta Arithmetica, Tome 163 (2014) no. 3, pp. 199-201. doi: 10.4064/aa163-3-1

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