I am trying to understand the dynamics of the aliquot sum.
I am wondering if a recurrence relation exists?
For example, would this work:
- Let $s(x)$ be the aliquot sum for $x$
- Let $p$ be a prime
- If $x$ is $1$, then $s(x)=0$
- If $x$ is prime, then $s(x)=1$
- If $p \nmid x$, then $s(px) = s(x) + ps(x) + x$
- If $p | x$, then $s(px) = s(x) + x$
Edit: Made updates based on comments received by Mason.