A Menon-type identity using Klee's function

Abstract

Menon's identity is a classical identity involving gcd sums and the Euler totient function $\varphi$. A natural generalization of $\varphi$ is the Klee's function ${\Phi }_s$. In this paper we derive a Menon-type identity using Klee's function and a generalization of the gcd function. This identity generalizes an identity given by Lee and Kim in [\textit{J. Number Theory 175, 42--50(2017)}].