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).
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.
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.
-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).
