e-Perfect Number
A number 
is called an 
-perfect number if 
, where 
is the sum of the e-Divisors of 
. If 
is squarefree, then 
. As a result, if 
is 
-perfect and 
is squarefree with 
, then 
is 
-perfect.
The first few 
-perfect numbers are 36, 180, 252, 396, 468, ... (OEIS A054979). There are no odd 
-perfect numbers. The first few primitive 
-perfect numbers are 36, 1800, 2700, 17424, ... (OEIS A054980).
REFERENCES:
Guy, R. K. "Exponential-Perfect Numbers." §B17 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 73, 1994.
Sloane, N. J. A. Sequences A054979 and A054980 in "The On-Line Encyclopedia of Integer Sequences."
Subbarao, M. V. and Suryanarayan, D. "Exponential Perfect and Unitary Perfect Numbers." Not. Amer. Math. Soc. 18, 798, 1971.
