Divisibility and Sequence Properties of $σ^+$ and $\varphi^+$

Published 6 Aug 2025 in math.GM | (2508.11660v1)

Abstract: Inspired by Lehmer's and Deaconescu's conjectures concerning Euler's totient function $\phi(n)$ and Schemmel's totient function $S_2(n)$, respectively, we investigate analogous divisibility problems involving $\sigma(n)$,$\sigma^+(n)$ and $\varphi^+(n)$. Further, we establish some interesting properties of the sequences $\left{\sigma^{+(n)\right}_{n=1}^\infty$} and $\left{\varphi^{+(n)\right}_{n=1}^\infty$.}