Yanapat Tongron and Narakorn Rompurk Kanasri

DOI: 10.14456/sjst-psu.2022.62

pp. 450 - 458

Abstract

For positive integers k, m, and n, let S_k^m(n) be the sum of all elements in the finite set {x^k: 1 ≤ x ≤ n⁄m , (x, n) = 1}. The formula for S_k^m(n) is established and simpler formulae for S_k^m(n under some conditions on m and n are verified. The explicit formulae for S₁^2a(n) and S₂^2a(n), where 2^a|n and a ≥ 1, are also provided.

Keywords

• arithmetic function
• Euler’s phi-function
• Möbius function
• Möbius inversion formula