The Explicit Formula and Parity for Some Generalized Euler Functions

Abstract

Based on elementary methods and techniques, the explicit formula for the generalized Euler function ${\phi }_e(n)(e=8,12)$ is given, and then a sufficient and necessary condition for ${\phi }_8(n)$ or ${\phi }_{12}(n)$ to be odd is obtained, respectively.

19pages,2 figures