  The abundancy index of a positive integer is the ratio between the sum of its
divisors and itself. We generalize previous results on abundancy indices by
defining a two-variable abundancy index function as
$I(x,n)\colon\mathbb{Z^+}\times\mathbb{Z^+}\to\mathbb{Q}$ where
$I(x,n)=\frac{\sigma_x(n)}{n^x}$. Specifically, we extend limiting properties
of the abundancy index and construct sufficient conditions for rationals
greater than one that fail to be in the image of the function $I(x,n)$.
