| Abstrakt: |
Let N denote the set of all positive integers. For j, n 2 N, let (j, n) and [j, n] respectively denote their gcd and lcm. If S ⊆ N and α is a real number then define LS,α(n) to be the sum of [j, n]α, where j 2 {1, 2, 3, . . ., n} for which (j, n) 2 S. In this paper we obtain asymptotic formulae for the summatory functions of LS,a(n) and LS,-a(n), where a 2 N and a ∊ 2. Apart from deducing some results proved earlier for S = N by Ikeda and Matsuoka, certain new asymptotic formulae are obtained here. [ABSTRACT FROM AUTHOR] |
