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;
}
}