  A positive integer $n$ is called perfect if $ \sigma(n)=2n$, where
$\sigma(n)$ denote the sum of divisors of $n$. In this paper we study the ratio
$\frac{\sigma(n)}{n}$. We define the function Abundancy Index $I:\mathbb{N} \to
\mathbb{Q}$ with $I(n)=\frac{\sigma(n)}{n}$. Then we study different properties
of the Abundancy Index and discuss the set of Abundancy Index. Using this
function we define a new class of numbers known as superabundant numbers.
Finally, we study superabundant numbers and their connection with Riemann
Hypothesis.
