In this article, based on ideas and results by Sándor (J Inequal Pure Appl Math 2:Art. 3, 2001; J Inequal Pure Appl Math 5, 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-\(T_0T^*\)-perfect numbers defined by Das and Saikia (Notes Number Theory Discrete Math 19:37–42, 2013) in details.
Perfect numbers Unitary perfect number Multiplicative perfect number E-perfect number Divisor function
Mathematics Subject Classification
Primary 11A25 Secondary 11A41 11B99
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The authors are grateful to an anonymous referee for valuable comments and for pointing them to some references. The second author is grateful to the excellent facilities provided to him by The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy), where this work was initiated.