Functiones et Approximatio Commentarii Mathematici

A short remark on consecutive coincidences of a certain multiplicative function

Winfried Kohnen

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We study integral solutions $n$ of the equation $A(n+k)=A(n)$, where $A$ is a certain multiplicative function related to Jordan's totient function.

Article information

Funct. Approx. Comment. Math., Volume 58, Number 1 (2018), 117-120.

First available in Project Euclid: 5 May 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors
Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas

multiplicative function Jordan's totient function


Kohnen, Winfried. A short remark on consecutive coincidences of a certain multiplicative function. Funct. Approx. Comment. Math. 58 (2018), no. 1, 117--120. doi:10.7169/facm/1659.

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  • D. Andrica and M. Piticari, On some extensions of Jordan's arithmetical functions, Acta universitatis Apulensis (7) (2004).
  • T.M. Apostol, Introduction to Analytic Number Theory, Undergrade texts in Mathematics, Springer 1976.
  • J. Bayless and T. Klyve, Reciprocal sums as a knowledge metric: Theory, computation, and perfect numbers, Amer. Math. Monthly 120(9) (2013), 822–831.
  • J. Bayless and P. Kinlaw, Consecutive coincidences of Euler's function, Int. J. Number Theory 12 (2016), no. 4, 1011–1026.
  • S.W. Graham, J.J. Holt and C. Pomerance, On the solutions to $\phi(n)=\break\phi(n+k)$, in: Number Theory in Progress, vol. 2 (Zakopane-Koscielisko, 1997), de Gruyter 1999, pp. 867–882.