Floor quotient grouping

An algorithm for evaluating sums that depend on $\lfloor N/i\rfloor$. If $q=\lfloor N/l\rfloor$, then all indices from $l$ through $r=\lfloor N/q\rfloor$ have quotient $q$. Jumping to $r+1$ visits only $O(\sqrt{N})$ blocks rather than all $N$ indices.