Given $i < n/2$ and denoting $[x]$ to be an integer part of $x$ (floor$(x)$) and $(a \operatorname{rem} b)$ to be a reminder when $a$ is divided by $b$.
$$ T(n,i) = \left(\left\lfloor\frac{n-i}{i}\right\rfloor \cdot i\right) + T\left(i + (n \operatorname{rem} i), (n \operatorname{rem} i)\right) $$ then is $T(n,i) = O(n)$?