A number is called an -perfect number if , where is the Sum of the e-Divisor of . If is Squarefree, then . As a result, if is -perfect and is Squarefree with , then is -perfect. There are no Odd -perfect numbers.
See also e-Divisor
References
Guy, R. K. ``Exponential-Perfect Numbers.'' §B17 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 73, 1994.
Subbarao, M. V. and Suryanarayan, D. ``Exponential Perfect and Unitary Perfect Numbers.''
Not. Amer. Math. Soc. 18, 798, 1971.