CF757E Bash Plays with Functions

CF757E Bash Plays with Functions

\[f_0(n) = \sum_{uv = n} [u ⊥ v] \]

\[f_r(n) = \sum_{uv = n} \frac{f_{r - 1}(u) + f_{r - 1}(v)}{2} \]

\(1 \le n \le 10 ^ 6\)。

CODE

\[f_r(n) = \sum_{u | n} f_{r - 1}(u) = \sum_{u | n} \left(\prod_{p ^ c | u} 2\right) \left(\prod_{p ^ c | \frac n u} \binom{c + r - 1}{r - 1}\right) \]

预处理逆元和质因数分解。