DIVCNTK - Counting Divisors (general)

$\sigma_0(i)$ 表示$i$ 的约数个数 求$S_k(n)=\sum_{i=1}^n\sigma_0(i^k)\mod 2^{64}$ 多测,$T\le10^4,n,k\le10^{10}$ Translated by @Kelin

Let $\sigma_0(n)$ be the number of positive divisors of $n$. For example, $\sigma_0(1) = 1$ , $\sigma_0(2) = 2$ and $\sigma_0(6) = 4$. Let $S_k(n) = \sum _{i=1}^n \sigma_0(i^k)$. Given $n$ and $k$ , find $S_k(n) \bmod 2^{64}$.

There are multiple test cases. The first line of input contains an integer $ T $ ( $ 1 \le T \le 10000 $ ), indicating the number of test cases. For each test case: The first line contains two integers $ n $ and $ k $ ( $ 1 \le n, k \le 10^{10} $ ).

For each test case, output a single line containing $ S_k(n) \bmod 2^{64} $ .

5
1 3
2 3
3 3
10 3
100 3

1
5
9
73
2302

+ Input #1: $1\leq n\leq 10000,TL=1s$ + Input #2: $1\leq T\leq 300,1\leq n\leq 10^{7},TL=5s$ + Input #3: $1\leq T\leq 75,1\leq n\leq 10^{8},TL=5s$ + Input #4: $1\leq T\leq 15,1\leq n\leq 10^{9},TL=5s$ + Input #5: $1\leq T\leq 5,1\leq n\leq 10^{10},TL=5s$