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\begin{abstract}
The abundancy index of a positive integer $n$ is defined to be the
rational number $I(n)=\sigma(n)/n$, where $\sigma$ is the sum of
divisors function $\sigma(n)=\sum_{d|n}d$.  An abundancy outlaw is
a rational number greater than 1 that fails to be in the image of
of the map $I$. In this paper, we consider rational numbers of the
form $(\sigma(N)+t)/N$ and prove that under certain conditions
such rationals are abundancy outlaws.
\end{abstract}

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