e-Perfect Number

A number $n$ is called an $e$-perfect number if $\sigma_e(n)=2n$, where $\sigma_e(n)$ is the Sum of the e-Divisor of $n$. If $m$ is Squarefree, then $\sigma_e(m)=m$. As a result, if $n$ is $e$-perfect and $m$ is Squarefree with $m\perp b$, then $mn$ is $e$-perfect. There are no Odd $e$-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.