Question 163
Let $n$ be a positive odd integer. Prove that
$$
\left\lfloor\log _{2} n\right\rfloor+\left\lfloor\log _{2}(n / 3)\right\rfloor+\left\lfloor\log _{2}(n / 5)\right\rfloor+\left\lfloor\log _{2}(n / 7)\right\rfloor+\cdots+\left\lfloor\log _{2}(n / n)\right\rfloor=(n-1) / 2 .
$$
$$
\left\lfloor\log _{2} n\right\rfloor+\left\lfloor\log _{2}(n / 3)\right\rfloor+\left\lfloor\log _{2}(n / 5)\right\rfloor+\left\lfloor\log _{2}(n / 7)\right\rfloor+\cdots+\left\lfloor\log _{2}(n / n)\right\rfloor=(n-1) / 2 .
$$