Definition:Abundancy Index

Definition
Let $n$ be a positive integer.

Let $\map {\sigma_1} n$ be the divisor sum function of $n$.

That is, let $\map {\sigma_1} n$ be the sum of all positive divisors of $n$.

Then the abundancy index of $n$ is defined as $\dfrac {\map {\sigma_1} n} n$.

Also see

 * Definition:Abundance