Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.5

On the Solutions of σ(n) = σ(n + k)

Andreas Weingartner
Department of Mathematics
Southern Utah University
Cedar City, Utah 84720


Given a fixed even integer k, we show that Schinzel's hypothesis H implies that σ(n) = σ(n + k) infinitely often. We also discuss the case of odd k and the more general equation σα(n) = σα(n + k).

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(Concerned with sequences A002961 A007373 A015863 A015866 A015876 A015880 A015882 A181647.)

Received February 26 2011; revised version received May 2 2011. Published in Journal of Integer Sequences, May 3 2011.

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