On the problem sigma(od)(n) = sigma(od)(n+1)

Abstract

Let sigma(od)(n) = Sigma(d vertical bar n,2 inverted iota d) d. In this paper, we study the solutions of sigma(od)(n) = sigma(od)(n + 1), their relations to Pell numbers, and some interesting conjectures. Finally, we obtain that the equation sigma(od)(n) = sigma(od)(n + 1) = sigma(od)(n + 2) equivalent to 1 (mod 2) has no solution.