On the problem σod(n) = σod(n+1)

Abstract

Let σ od (n) = d|n,2 d d. In this paper, we study the solutions of σ od (n) = σ od (n + 1), their relations to Pell numbers, and some interesting conjectures. Finally, we obtain that the equation σ od (n) = σ od (n + 1) = σ od (n + 2) ≡ 1 (mod 2) has no solution.