trainging contest#1（2011大连现场赛）I BY bly

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long LL;
const LL mod=1000000007;
int vis[1000010],c;
LL rev;
int prime[1000000];
LL pow_mod(LL n)
{
if(n==0) return 1;
LL ans=pow_mod(n/2);
ans=ans*ans%mod;
if(n%2==1) ans=ans*30%mod;
return ans;
}
void init()
{
memset(vis,0,sizeof(vis));
c=0;rev=pow_mod(mod-2);
for(int i=2;i<=1000;i++) if(!vis[i])
{
for(int j=i*i;j<=1000000;j+=i) vis[j]=1;
}
for(int i=2;i<=1000000;i++) if(!vis[i])
prime[c++]=i;
}
LL getsum(LL x)
{
LL t1=(x*x%mod+x)%mod;
LL t2=(2*x%mod+1)%mod;
LL t3=((3*x)%mod*x%mod+3*x%mod-1+mod)%mod;
return ((t1*t2%mod)*t3%mod)*rev%mod;
}
LL getfour(LL x)
{
return ((x*x%mod)*x%mod)*x%mod;
}
int fac[100],f,n;
int main()
{
init();
int T;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
int tmp=n;
f=0;
for(int i=0;i<c;i++)
{
if(tmp%prime[i]==0) fac[f++]=prime[i];
while(tmp%prime[i]==0) tmp/=prime[i];
}
if(tmp!=1) fac[f++]=tmp;
LL ans=getsum(n);
for(int i=1;i<(1<<f);i++)
{
int bitcount=0,a=1;
for(int j=0;j<f;j++) if(i&(1<<j))
{
a*=fac[j];
bitcount++;
}
LL t=getfour(a)*getsum(n/a)%mod;
if(bitcount%2==1) ans=(ans-t+mod)%mod;
else ans=(ans+t)%mod;
}
printf("%lld\n",ans);
}
return 0;
}