Journal of Integer Sequences, Vol. 15 (2012), Article 12.4.1

Giuga Numbers and the Arithmetic Derivative

José María Grau
Departamento de Matematicas
Universidad de Oviedo
Avda. Calvo Sotelo, s/n
33007 Oviedo

Antonio M. Oller-Marcén
Centro Universitario de la Defensa
Ctra. de Huesca, s/n
50090 Zaragoza


We characterize Giuga numbers as solutions to the equation n' = an + 1, with aN and n' being the arithmetic derivative. Although this fact does not refute Lava's conjecture, it does suggest doubts about its veracity.

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(Concerned with sequences A003415 A007850.)

Received March 11 2011; revised version received March 26 2012. Published in Journal of Integer Sequences, March 26 2012.

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