GCD Extreme (hard)
This problem is a harder version of GCDEX.
Let
$$G(n) = \sum _{i=1}^{n} \sum _{j=i+1}^{n} \gcd(i, j).$$
For example, $G(1) = 0$, $G(2) = \gcd(1, 2) = 1$, $G(3) = \gcd(1, 2) + \gcd(1, 3) + \gcd(2, 3) = 3$.
Given $N$, find $G(N)$ modulo $2^{64}$.
Input
First line of contains $T$ ($1 \le T \le 10000$), the number of test cases.
Each of the next $T$ lines contains a single integer $N$. ($1 \le N \le 235711131719$)
Output
For each number $N$, output a single line containing $G(N)$ modulo $2^{64}$.
Example
Input
5
1
4
100
1000000
100000000000
Output
0
7
13015
4071628673912
5482289417216306300
Explanation for Input
- $G(4) = \gcd(1, 2) + \gcd(1, 3) + \gcd(1, 4) + \gcd(2, 3) + \gcd(2, 4) + \gcd(3, 4) = 7$.
- $G(10^{11}) = 75710919967921216138364 \equiv 5482289417216306300 \pmod{2^{64}}$.
Information
There are 7 Input files.
- Input #0: $1 \le T \le 10000$, $1 \le N \le 10000$, TL = 1s.
- Input #1: $1 \le T \le 1000$, $1 \le N \le 10^{7}$, TL = 20s.
- Input #2: $1 \le T \le 200$, $1 \le N \le 10^{8}$, TL = 20s.
- Input #3: $1 \le T \le 40$, $1 \le N \le 10^{9}$, TL = 20s.
- Input #4: $1 \le T \le 10$, $1 \le N \le 10^{10}$, TL = 20s.
- Input #5: $1 \le T \le 2$, $1 \le N \le 10^{11}$, TL = 20s.
- Input #6: $T = 1$, $1 \le N \le 235711131719$, TL = 20s.
My solution runs in 10.7 sec. (total time)
Source Limit is 10 KB.