The abundancy index of a positive integer

is defined to be the
rational number

, where

is the sum of
divisors function

. An abundancy outlaw is
a rational number greater than 1 that fails to be in the image of
of the map

. In this paper, we consider rational numbers of the
form

and prove that under certain conditions
such rationals are abundancy outlaws.
Received October 25 2006;
revised version received August 31 2007; September 25 2007.
Published in Journal of Integer Sequences, September 25 2007.