JIPAM

A Note on Multiplicatively $e$-perfect Numbers  
 
  Authors: Le Anh Vinh, Dang Phuong Dung,  
  Keywords: Perfect number, Exponential divisor, Multiplicatively perfect, Sum of divisors, Number of divisors.  
  Date Received: 17/10/05  
  Date Accepted: 26/10/05  
  Subject Codes:

11A25, 11A99.

  
  Editors: Jozsef Sandor,  
 
  Abstract:

Let $ T_e ( n )$ denote the product of all exponential divisors of $ n$. An integer $ n$ is called multiplicatively $ e$-perfect if $ T_e ( n ) = n^2$ and multiplicatively $ e$-superperfect if $ T_e ( T_e ( n ) ) = n^2$. In this note, we give an alternative proof for characterization of multiplicatively $ e$-perfect and multiplicatively $ e$-superperfect numbers.;


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