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

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Abstract

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

Article information

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

Dates
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
https://projecteuclid.org/euclid.involve/1511370944

Digital Object Identifier
doi:10.2140/involve.2015.8.745

Mathematical Reviews number (MathSciNet)
MR3404653

Zentralblatt MATH identifier
1367.11014

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

Keywords
sum of divisors Euler function

Citation

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. https://projecteuclid.org/euclid.involve/1511370944


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References

  • 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.