11762

#include <iostream>

#include <vector>
#include <map>
#include <stdio.h>

using namespace std;

int prime[1000001];
int primes[1000001];
double dp[1000001];
vector<int> vb;
map<int,int> mp;

int main()
{
int n,t;

primes[0]=primes[1]=0;

for(int i=2;i*i<1000001;i++)
{
if(prime[i]==0)
{
for(int j=i*i;j<1000001;j+=i)
{
prime[j]=1;
primes[j]=i;
}
//primes[i]=i;
}
}

prime[0]=prime[1]=0;
for(int i=2;i<1000001;i++)
{
if(primes[i]==0)
primes[i]=i;
if(prime[i])
prime[i]=0;
else
prime[i]=1;
prime[i]+=prime[i-1];
}

dp[1]=0;

for(int i=2;i<1000001;i++)
{
int k=i;
mp.clear();
vb.clear();
while(primes[k]!=0)
{
if(mp[primes[k]]==0)
{
mp[primes[k]]=1;
vb.push_back(primes[k]);
}
k/=primes[k];
}

double g=0;
for(int j=0;j<vb.size();j++)
g+=dp[i/vb[j]];

dp[i]=(g+prime[i])/vb.size();
}
cin>>t;
int c=0;
while(t--)
{
cin>>n;
//cout<<prime[n]<<"\n";
c++;
cout<<"Case "<<c<<": ";
printf("%.10lf\n",dp[n]);
}

return 0;
}

 

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