A+ CATEGORY SCIENTIFIC UNIT

On the sum of the first $n$ values of the Euler function

Volume 163 / 2014

R. Balasubramanian, Florian Luca, Dimbinaina Ralaivaosaona Acta Arithmetica 163 (2014), 199-201 MSC: Primary 11N37. DOI: 10.4064/aa163-3-1

Abstract

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 $E(n)$.

Authors

  • R. BalasubramanianThe Institute of Mathematical Sciences
    Chennai 600 113, India
    e-mail
  • Florian LucaMathematical Institute
    UNAM Juriquilla
    76230 Santiago de Querétaro, México
    and
    School of Mathematics
    University of the Witwatersrand
    P.O. Box Wits 2050
    Johannesburg, South Africa
    e-mail
  • Dimbinaina RalaivaosaonaAfrican Institute for Mathematical Sciences
    6 Melrose Ave.
    Muizenberg, South Africa
    e-mail

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