A generalization of Menon's identity with Dirichlet characters

Yan Li, Xiaoyu Hu, Daeyeoul Kim

The classical Menon's identity [7] states that \begin{equation*}\label{oldbegin1} \sum_{\substack{a\in\Bbb Z_n^\ast }}\gcd(a -1,n)=φ(n) σ_{0} (n), \end{equation*} where for a posit…