## e-Perfect Number

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.

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.