Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 1, pp. 29-38 (1995)

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On Generalized Landau Identities

Pentti Haukkanen

Department of Mathematical Sciences, University of Tampere,
P.O. Box 607, SF-33101 Tampere - FINLAND

Abstract: The identity $$ \sum_{d|r}\frac{\mu^{2}(d)}{\phi(d)}=\frac{r}{\phi(r)}, $$ 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: Number-theoretic 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.

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