Definition:Abundance

Definition
Let $n \in \Z_{\ge 0}$ 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 abundance of $n$ is defined as $\map A n = \map {\sigma_1} n - 2 n$.

Also see

 * Definition:Abundancy Index