Comet OJ - Contest #8 E.神奇函数

Posted 2020-11-21 gmh77

旧题解：https://blog.csdn.net/gmh77/article/details/99066792#commentBox

之前写的有些奇怪，不能体现这道题的sb所以再推一遍

(ecause n=sum_{d mid n}{varphi(d)})

( herefore sum_{i=1}^{n}{f(i)}=sum_{n}{prod{{a_i}^{left lfloor frac{p_i}{2} ight floor}}})

(=sum_{n}{sum_{prod{{a_i}^{left lfloor frac{p_i}{2} ight floor}} mid d}{varphi(d)}})

(=sum_{d=1}^{left lfloor sqrt{n} ight floor}{varphi(d)sum_{n}{[d^2mid n]}})$

(=sum_{d=1}^{left lfloor sqrt{n} ight floor}{varphi(d)*left lfloor frac{n}{d^2} ight floor})