For positive integers k, m, and n, let Skm(n) be the sum of all elements in the finite set {xk: 1 ≤ x ≤ n⁄m , (x, n) = 1}. The formula for Skm(n) is established and simpler formulae for Skm(n under some conditions on m and n are verified. The explicit formulae for S12a(n) and S22a(n), where 2a|n and a ≥ 1, are also provided.
