Some Results on Generalized Multiplicative Perfect Numbers

In this article, based on ideas and results by J. S'andor (2001, 2004), we define $k$-multiplicatively $e$-perfect numbers and $k$-multiplicatively $e$-superperfect numbers and prove some results on them. We also characterize the $k$-$T_0{T}^{\ast }$-perfect numbers defined by Das and Saikia (2013) in details.