On two new arithmetic functions and the k-power complement number sequences *. From: Scientia Magna | Date: January 1, 2005| Author: | COPYRIGHT 2005 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.  All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information) Copyright information

Abstract The main purpose of this paper is to study the asymptotic property of the k-power complement numbers (where k [greater than or equal to] 2 is a fixed integer), and obtain some interesting asymptotic formulas.

Keywords: k-power complement number; Asymptotic formula; Arithmetic function.

[section] 1. Introduction

Let k [greater than or equal to] 2 is a fixed integer, for each integer n, let C(n) denotes the smallest integer such that n x C(n) is a perfect k-power, C(n) is called k-power complement number of n. In problem 29 of reference [1], Professor F. ...

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