PORTUGALIAE MATHEMATICA Vol. 52, No. 1, pp. 2938 (1995) 

On Generalized Landau IdentitiesPentti HaukkanenDepartment of Mathematical Sciences, University of Tampere,P.O. Box 607, SF33101 Tampere  FINLAND Abstract: The identity $$ \sum_{dr}\frac{\mu^{2}(d)}{\phi(d)}=\frac{r}{\phi(r)}, $$ where $\mu$ is the Möbius function and $\phi$ is the Euler function, is known in the literature as the Landau identity. The present paper collects several extensive generalizations of that identity given by the author and P.J. McCarthy. Some of the extensive generalizations are further generalized. Also a large number of known special cases of the identities here are listed. Keywords: Numbertheoretic identities; even arithmetical functions; regular convolutions; Möbius function; Euler totient; Ramanujan sums. Classification (MSC2000): 11A25 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1995 Sociedade Portuguesa de Matemática
