#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int maxn=1e6+10;
const LL mod=1e9+7;
int phi[maxn], p[maxn+1];
bool check[maxn];

int phi_and_prime_table()
{
    phi[1]=1;
    int sz=0;
    for(int i=2;i<maxn;i++)
    {
        if(!p[i]) p[++sz]=i,phi[i]=i-1;
        
 
for(int j=1;j<=sz&&p[j]<=maxn/i;j++) //註意這個等號不能丟 因為這個wa了很多發 p[maxn+1]數組大小+1可以這麽寫 不然就老老實實 if break 或者加個LL
        {
            p[i*p[j]]=1;
            if(i%p[j]==0) {
                phi[i*p[j]]=phi[i]*p[j];break;
            }
            phi[i*p[j]]=phi[i]*(p[j]-1);
        }
    }
    
 
return sz;
}
#define vii vector<int>
vii fac[maxn];
void getfactor(LL x)
{
    vii &f=fac[x];
    for(int i=1;(LL)p[i]*p[i]<=x;i++)
    {
        if(x%p[i]==0)
        {
            f.push_back(p[i]);
            while(x%p[i]==0) x/=p[i];
        }
    }
    if(x!=1)f.push_back(x);
}
LL cal(
 
int now,LL cur,LL n,vii &f)
{

    if(now==f.size())return 0;
    LL r=0;
    for(int i=now;i<f.size();i++)
    {
        r+=n/(cur*f[i])-cal(i+1,cur*f[i],n,f);
    }
    return r;
}

int main() {
    #ifdef shuaishuai
    freopen("in.txt","r",stdin);
    #endif //  shuaishuai
    int t;
    scanf("%d",&t);
    phi_and_prime_table();
    for(int i=2;i<maxn;i++){
        getfactor(i);
    }
    for(int cas=1;cas<=t;cas++)
    {
        LL n;
        scanf("%lld",&n);
        LL ans=0;
        for(LL i=1;i*i<n;i++)
        {
            ans+=n/i-cal(0,1,n/i,fac[i])-phi[i];
            assert(ans>=0);
        }
        printf("Case #%d: %lld\n",cas,(ans*2+1)%mod);
    }
    return 0;
}

HDU 5942 Just a Math Problem CCPC 2016 杭州