Today I stumbled upon the following Question: Is there a function $f\colon \mathbb N^+ \to \mathbb N^+$ such that $f(f(n))=``\text{number of divisors of }n"$. We have already deduced that
- $f(1)=1$
- $f(2)=2$
- if $p$ is prime then $f(p)$ is also prime
- every number mapped to 2 is a prime
- if $f(p)=2$ then there is some prime $q$ such that $f(q)=p$
- clearly $f$ is surjective
