Geodesic
Abundancy "outlaws" of the form $\frac{(\sigma(N)+t)}{N}$
Journal of integer sequences, Tome 10 (2007) no. 9.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\sigma(n)=\sum_{d\vert n}d$. 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.
Classification : 11A25, 11Y55, 11Y70
Keywords: abundancy index, abundancy outlaw, sum of divisors function, perfect numbers 
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     author = {Stanton, William G. and Holdener, Judy A.},
     title = {Abundancy "outlaws" of the form $\frac{(\sigma(N)+t)}{N}$},
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Stanton, William G.; Holdener, Judy A. Abundancy "outlaws" of the form $\frac{(\sigma(N)+t)}{N}$. Journal of integer sequences, Tome 10 (2007) no. 9. http://geodesic.mathdoc.fr/item/JIS_2007__10_9_a1/