OMC100(C)

　つねに $$\left\lceil \frac{i+1}{j} \right\rceil-\left\lfloor \frac{i}{j} \right\rfloor=1$$ が成り立つから， $$\begin{aligned} \Biggl(\sum_{i=1}^{10^6+1}\sum_{j=1}^{10^6+1}{\left\lceil \frac{i}{j} \right\rceil}\Biggr)-\Biggl(\sum_{i=1}^{10^6}\sum_{j=1}^{10^6}{\left\lfloor \frac{i}{j} \right\rfloor}\Biggr) &=\sum_{i=1}^{10^6}\sum_{j=1}^{10^6}\Biggl(\left\lceil\frac{i+1}{j} \right\rceil-\left\lfloor \frac{i}{j}\right\rfloor\Biggr)+\sum_{j=1}^{10^6+1}{\left\lceil \frac{1}{j} \right\rceil}+\sum_{i=1}^{10^6}\left\lceil \frac{i+1}{10^6+1} \right\rceil\\ &=(10^6)^2+(10^6+1)+10^6\\ &=\textbf{1000002000001}. \end{aligned}$$