A Menon-type identity using Klee's function

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 ${\mathrm{\Phi }}_s$. 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 [$\mathit{\text{J.}}\mathit{\text{Number}}\mathit{\text{Theory}}\mathit{\text{175,}}\mathit{\text{42–50(2017)}}$].