Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 5 (2015), 745-748.

Power values of the product of the Euler function and the sum of divisors function

Luis Elesban Santos Cruz and Florian Luca

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We find examples of positive integers n such that ϕ(n3)σ(n3) is a perfect square.

Article information

Involve, Volume 8, Number 5 (2015), 745-748.

Received: 19 October 2013
Revised: 29 August 2014
Accepted: 7 September 2014
First available in Project Euclid: 22 November 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11B68: Bernoulli and Euler numbers and polynomials 11A25: Arithmetic functions; related numbers; inversion formulas

sum of divisors Euler function


Santos Cruz, Luis Elesban; Luca, Florian. Power values of the product of the Euler function and the sum of divisors function. Involve 8 (2015), no. 5, 745--748. doi:10.2140/involve.2015.8.745.

Export citation


  • F. Beukers, F. Luca, and F. Oort, “Power values of divisor sums”, Amer. Math. Monthly 119:5 (2012), 373–380.
  • K. Broughan, K. Ford, and F. Luca, “On square values of the product of the Euler totient and sum of divisors functions”, Colloq. Math. 130:1 (2013), 127–137.
  • P. van Emde Boas and D. Kruyswijk, “A combinatorial problem on finite Abelian groups”, Math. Centrum Amsterdam Afd. Zuivere Wisk. 1967:ZW-009 (1967), 27.
  • T. Freiberg, “Products of shifted primes simultaneously taking perfect power values”, J. Aust. Math. Soc. 92:2 (2012), 145–154.
  • J. E. Olson, “A combinatorial problem on finite abelian groups, II”, J. Number Theory 1 (1969), 195–199.