# BZOJ 3560

Orz PoPoQQQ 里面似乎有些错误的说

$$\sum_{i_1=0}^{b_1}\sum_{i_2=0}^{b_2}\cdots \sum_{i_n=0}^{b_n}\varphi(p^{\sum_{j=1}^n i_j})$$

2 3 5
$2^0 2^0 2^0$ $3^0 3^0 3^0$ $5^0 5^0 5^0$
$2^0 2^0 2^1$ $3^0 3^0 3^1$ $5^0 5^0 5^1$
$2^0 2^1 2^0$ $3^1 3^0 3^0$ $5^0 5^1 5^0$
$2^0 2^1 2^1$ $3^1 3^0 3^1$ $5^0 5^1 5^1$

2 3 5
$\varphi(1)=1$ $\varphi(1)=1$ $\varphi(1)=1$
$\varphi(2)=1$ $\varphi(3)=2$ $\varphi(5)=4$
$\varphi(2)=1$ $\varphi(3)=2$ $\varphi(5)=4$
$\varphi(4)=2$ $\varphi(9)=6$ $\varphi(25)=20$

$$((\sum_{i_1=0}^{b_1}\sum_{i_2=0}^{b_2}\cdots \sum_{i_n=0}^{b_n}p^{\sum_{j=1}^n i_j})-1)\times \frac{p-1}{p}+1$$

$$((\prod_{i=1}^n \sum_{j=0}^{b_i} p^j)-1)\times \frac{p-1}{p}+1$$