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A number 
 is called a 
 
-perfect number if 
, where 
 is the Sum of the
e-Divisor of 
.
See also e-Divisor, e-Perfect Number
References
Guy, R. K.  ``Exponential-Perfect Numbers.''  §B17 in
  Unsolved Problems in Number Theory, 2nd ed.  New York: Springer-Verlag, p. 73, 1994.