A Divisor-Sum Analogue of the Collatz Map

Ritesh Dwivedi, Rohit Yadav

Let $\sigma$ denote the sum-of-divisors function and let $\mathcal{R}$ send an odd integer $n$ to $\sigma (n)$ and an even integer $n$ to $n/2$. We conjecture that every orbit of $\mathcal{R}…