Some Inequalities About Certain Arithmetic Functions

Abstract

Let

.(e) k (n) denote the sum of kth powers of the exponential divisors of n, .(e) (n) denote the number of the exponential divisors of n, .(e) k (n) denote the sum of kth powers of the e− unitary divisors of n and .(e). (n) denote the number of the e− unitary divisors of n. The purpose of this paper is to present several inequalities about the arithmetic functions . (e) k , .(e), . (e). k , .(e). and other well-known arithmetic functions. Among these, we have the following: . (e) k (n) . k (n) h1k + 2k + ... + 􀀀.(e) (n).ki and .k (n) + nk . . (e) k (n) + .. k (n) , for any n . 1 and k . 0.