Unitary Analogues of Some Arithmetic Functions

Pussadee Yangklan, Vichian Laohakosol, Pattira Ruengsinsub, Sukrawan Mavecha

Abstract

A number of arithmetic functions, referred to as the generalized unitary-Euler’s totient, generalized unitary-Cohen’s totient, generalized unitary-divisor, generalized unitary-Liouville, odd-phi, and even-phi functions which generalize the classical totient, divisor and Liouville functions, are intro- duced in the setting of unitary convolution. Basic properties of these functions extending the existing ones are established. Results related to the problem of counting exponentially odd and exponentially even numbers are derived as applications.