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1038.cpp
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1038.cpp
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define PI (acos(-1))
#define ct cout<<
#define cn cin>>
#define spc <<" "<<
#define nl puts("")
#define _fl(x) puts("FLAG " #x);
#define _(x) cout<< #x <<" is "<< x <<endl;
#define fs first
#define sc second
#define pb push_back
#define all(v) (v).begin(), (v).end()
#define _109 (1000000000)
#define _0(arr) memset(arr,0,sizeof ( arr ) )
#define _1(arr) memset(arr,-1,sizeof ( arr ) )
#define _ninp(n,arr) for(int i=0; i<n;i++)cin>>arr[i];
#define _nout(n,arr) for(int i=0; i<n;i++)cout<<arr[i]<<" \n"[i==n-1];
double _eps=1e-6;
double dp[100000+100];
bool mark[100000+100];
void factor(vector<int> & res,int n){
for(ll j=2; j*j<=n; j++){
if(n%j==0){
res.pb(j);
if(j!=n/j)res.pb(n/j);
}
}
}
double f(int n){
if(n==1)return 0;
if(mark[n])return dp[n];
vector<int> fact;
factor(fact,n);
double res=0;
for(int fc:fact){
res+=f(n/fc);
}
double total=fact.size()+2;
res/=total;
res+=1;
res=(res*total)/(total-1);
mark[n]=true;
return dp[n]=res;
}
int main() {
int T;
cn T;
for(int caseno=1; caseno<=T ;caseno++){
int n;
cn n;
printf("Case %d: %.10f\n",caseno,f(n));
}
return 0;
}