On square values of the product of the Euler totient and sum of divisors functions

Tom 130 / 2013

Kevin Broughan, Kevin Ford, Florian Luca Colloquium Mathematicum 130 (2013), 127-137 MSC: Primary 11A41. DOI: 10.4064/cm130-1-11


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.


  • Kevin BroughanDepartment of Mathematics
    University of Waikato
    Private Bag 3105, Hamilton, New Zealand
  • Kevin FordDepartment of Mathematics
    The University of Illinois
    at Urbana-Champaign Urbana
    1409 West Green St.
    Champaign, IL 61801, U.S.A.
  • Florian LucaFundación Marcos Moshinsky
    Instituto de Ciencias Nucleares UNAM
    Circuito Exterior, C.U., Apdo. Postal 70-543
    México, D.F. 04510, Mexico

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