D Sigma Function

Sigma function is an interesting function in Number Theory. It is denoted by the Greek letter Sigma (σ). This function actually denotes the sum of all divisors of a number. For example σ(24) = 1+2+3+4+6+8+12+24=60. Sigma of small numbers is easy to find but for large numbers it is very difficult to find in a straight forward way. But mathematicians have discovered a formula to find sigma. If the prime power decomposition of an integer is

Then we can write,

For some n the value of σ(n) is odd and for others it is even. Given a value n, you will have to find how many integers from 1 to n have even value of σ.

Input
Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 1012).

Output
For each case, print the case number and the result.

Sample Input
4
3
10
100
1000
Sample Output
Case 1: 1
Case 2: 5
Case 3: 83
Case 4: 947

题解：

题目给这么长的公式。其实就是让你求1~n内有多少个约数和为偶数。
参考：http://www.cnblogs.com/xiaochaoqun/p/6616590.html
日后再来研究，根据大佬总结公式：n−n√−(√n/2)

代码：

#include <iostream>#include <algorithm>#include <cstdio>#include <cstring>#include <cmath>using namespace std;typedef long long LL;int main(){    int ks=1;    int T;    scanf("%d",&T);    LL n;    while(T--)    {       scanf("%lld",&n);       LL ans = n-(LL)sqrt(n)-(LL)sqrt(n/2);       printf("Case %d: %lld\n",ks++,ans);    }    return 0;}