On the mean value of the e-squarefree e-divisior function

Let [t.sup.(e)] (n) denote the number of e-squarefree e-divisor of n. The aim of the present paper is to establish an asymptotic formula for the mean value of the function ([t.sup.(e)])r, where r [greater than or equal to] 1 is a fixed integer. Keywords E-squarefree e-divisor function, the generalized divisor function, convolution method.
[section] 1. Introduction An integer d = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is called an e-divisor of n =[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] > 1 if [b.sub.i]|[a.sub.i] for [...]