PORTUGALIAE MATHEMATICA Vol. 56, No. 3, pp. 329343 (1999) 

Rational Arithmetical Functions of Order (2,1) with Respect to Regular ConvolutionsPentti HaukkanenDepartment of Mathematical Sciences, University of Tampere,P.O. Box 607, FIN33101 Tampere  FINLAND Abstract: S.S. Pillai's arithmetical function $P(n)=\sum_{m\ppmod n}(m,n)$ is an example of a rational arithmetical function of order $(2,1)$. We generalize $P(n)$ with respect to Narkiewicz's regular convolution and show that the generalized Pillai's function is an example of a rational arithmetical function of order $(2,1)$ with respect to Narkiewicz's regular convolution. We derive identities for rational arithmetical functions of order $(2,1)$ with respect to Narkiewicz's regular convolution and therefore also for Pillai's function and its generalization. Keywords: Rational arithmetical functions; Narkiewicz's regular convolution; Pillai's function; identical equations. Classification (MSC2000): 11A25. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 1999 Sociedade Portuguesa de Matemática
