Relatively Prime Powers

2000ms

262144K

Description:

Consider some positive integer $$$x$$$. Its prime factorization will be of form $$$x = 2^{k_1} \cdot 3^{k_2} \cdot 5^{k_3} \cdot \dots$$$

Let's call $$$x$$$ elegant if the greatest common divisor of the sequence $$$k_1, k_2, \dots$$$ is equal to $$$1$$$. For example, numbers $$$5 = 5^1$$$, $$$12 = 2^2 \cdot 3$$$, $$$72 = 2^3 \cdot 3^2$$$ are elegant and numbers $$$8 = 2^3$$$ ($$$GCD = 3$$$), $$$2500 = 2^2 \cdot 5^4$$$ ($$$GCD = 2$$$) are not.

Count the number of elegant integers from $$$2$$$ to $$$n$$$.

Each testcase contains several values of $$$n$$$, for each of them you are required to solve the problem separately.

Input:

The first line contains a single integer $$$T$$$ ($$$1 \le T \le 10^5$$$) — the number of values of $$$n$$$ in the testcase.

Each of the next $$$T$$$ lines contains a single integer $$$n_i$$$ ($$$2 \le n_i \le 10^{18}$$$).

Output:

Print $$$T$$$ lines — the $$$i$$$-th line should contain the number of elegant numbers from $$$2$$$ to $$$n_i$$$.

Sample Input:

Sample Output:

Note:

Here is the list of non-elegant numbers up to $$$10$$$:

$$$4 = 2^2, GCD = 2$$$;
$$$8 = 2^3, GCD = 3$$$;
$$$9 = 3^2, GCD = 2$$$.

The rest have $$$GCD = 1$$$.

Informação

Provedor Codeforces

Código CF1036F