Sigma Function (平方数与平方数*2的约数和是奇数)

Sigma Function

https://vjudge.net/contest/288520#problem/D

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<bits/stdc++.h>
 using namespace std;
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define sqr(x) ((x)*(x))
 #define pb push_back
 #define eb emplace_back
 #define maxn 100005
 #define eps 1e-8
 #define pi acos(-1.0)
 #define rep(k,i,j) for(int k=i;k<j;k++)
 typedef long long ll;
 typedef pair<int,int> pii;
 typedef pair<long long,int>pli;
 typedef pair<int,char> pic;
 typedef pair<pair<int,string>,pii> ppp;
 typedef unsigned long long ull;
 const long long mod=;
 /*#ifndef ONLINE_JUDGE
         freopen("1.txt","r",stdin);
 #endif */

 int pow_mul(ll a,ll b){
     int ans=;
     while(b){
         if(b&) ans=ans*a%;
         b>>=;
         a=a*a%;
     }
     return ans;
 }

 int main(){
     #ifndef ONLINE_JUDGE
      //   freopen("1.txt","r",stdin);
     #endif
   //  std::ios::sync_with_stdio(false);
     int t;
     cin>>t;
     for(int _=;_<=t;_++){
         ll n;
         cin>>n;
         int ans=;
         for(ll i=;i*i<=n;i++){
             ans++;
             if(i*i*<=n) ans++;
         }
         cout<<"Case "<<_<<": "<<n-ans<<endl;
     }
 }