Generalized Mobius-type functions and special set of k-free numbers

TL;DR

This paper explores new properties of generalized Mobius functions, introduces a special set of k-free numbers, and derives asymptotic formulas for their partial sums, expanding understanding of these number-theoretic functions.

Contribution

It presents novel properties of generalized Mobius functions and introduces a special set of k-free numbers with asymptotic analysis of their partial sums.

Findings

Derived asymptotic formulas for partial sums of generalized Mobius functions.

Identified new properties of these functions.

Defined a special set of k-free numbers with analytical results.

Abstract

In [3] Bege introduced the generalized Apostol's Mobius functions. In this paper we are presenting new properties of this functions. By introducing the special set of k-free numbers we have obtained some asymptotic formulas for the partial sums of these functions.