A Menon-type Identity concerning Dirichlet characters and a generalization of the gcd function

Arya Chandran, Neha Elizabeth Thomas, K Vishnu Namboothiri

Menon's identity is a classical identity involving gcd sums and the Euler totient function $\varphi$. In a recent paper, Zhao and Cao derived the Menon-type identity $\sum\limits_{\subst…