Totient chain

The sequence $n,\phi (n),\phi (\phi (n)),\dots ,1$ obtained by iterating Euler's totient function on a positive integer. Since $1\le \phi (n)<n$ for $n>1$, the sequence reaches 1. Counting both endpoints gives the length recurrence relation $L(1)=1$ and $L(n)=1+L(\phi (n))$; increasing order of $n$ therefore suffices for dynamic programming.