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
#include<iostream>
#include<cmath>
#include<cstdio>
using namespace std;
typedef long long ll;int main()
{int m;scanf("%d",&m);for(int a = 1;a <= m;a ++){ll n;scanf("%lld",&n);printf("Case %d: %lld\n",a,n-(ll)sqrt((double)n)-(ll)sqrt((double)n/2.0));}return 0;
}