Floor-division grouping

For a positive integer $n$, indices with the same quotient $q=\lfloor n/i\rfloor$ form intervals. If an interval begins at $l$, it ends at $r=\lfloor n/q\rfloor$. There are $O(\sqrt{n})$ distinct quotients: either $i\le \sqrt{n}$, or the quotient is below $\sqrt{n}$. This permits summing constant-quotient blocks instead of visiting every index.