Definition:Abundancy Index

Definition
Let $n$ be a positive integer.

Let $\sigma \left({n}\right)$ be the sigma function of $n$.

That is, let $\sigma \left({n}\right)$ be the sum of all positive divisors of $n$.

Then the abundancy of $n$ is defined as $\dfrac {\sigma \left({n}\right)} n$.

Perfect
A number is classified as perfect iff $\dfrac {\sigma \left({n}\right)} n = 2$.

Also see

 * Definition:Abundance