Problem 414

Erdős Problem #414: declared status 'open'. Formalized: yes. Let $h_1(n)=h(n)=n+\tau(n)$ (where $\tau(n)$ counts the number of divisors of $n$) and $h_k(n)=h(h_{k-1}(n))$. Is it true, for any $m,n$, there exist $i$ and $j$ such that $h_i(m)=h_j(n)$? Prize: no. OEIS: A064491. Tags: iterated functions, number theory.