Geodesic
On the solutions of $\sigma (n) = \sigma (n + k)$
Journal of integer sequences, Tome 14 (2011) no. 5.

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

Summary: Given a fixed even integer $k$, we show that Schinzel's hypothesis H implies that $\sigma (n) = \sigma (n + k)$ infinitely often. We also discuss the case of odd $k$ and the more general equation $\sigma _{\alpha }(n) = \sigma _{\alpha }(n + k)$.
Classification : 11A25
Keywords: sum-of-divisors function, schinzel's hypothesis H 
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     author = {Weingartner, Andreas},
     title = {On the solutions of $\sigma (n) = \sigma (n + k)$},
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     number = {5},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a0/}
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Weingartner, Andreas. On the solutions of $\sigma (n) = \sigma (n + k)$. Journal of integer sequences, Tome 14 (2011) no. 5. http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a0/