International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 648165, 15 pages
doi:10.1155/2010/648165
Research Article

Combinatorial Aspects of the Generalized Euler's Totient

Nittiya Pabhapote1 and Vichian Laohakosol2

1Department of Mathematics, University of the Thai Chamber of Commerce, Bangkok 10400, Thailand
2Department of Mathematics, Faculty of Science and Institute for Advanced Studies, Kasetsart University, Bangkok 10900, Thailand

Received 24 April 2010; Revised 29 July 2010; Accepted 6 August 2010

Academic Editor: Pentti Haukkanen

Copyright © 2010 Nittiya Pabhapote and Vichian Laohakosol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.