Question 8
Delete from the positive integers all multiples of four and all numbers one more than a multiple of four. Let $S_n$ be the sum of the first $n$ remaining terms. Compute $$\lfloor\sqrt{S_1}\rfloor+\lfloor\sqrt{S_2}\rfloor+\cdots+\lfloor\sqrt{S_{2006}}\rfloor,$$ where the floor is the greatest integer not exceeding its argument.