#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=5e6+10;
bool vis[maxn];
int prime[maxn/7];
int phi[maxn];
int mu[maxn];
int tot=0;
ll sum_phi[maxn];
int  sum_mu[maxn];
void get_mu_phi(){int n=maxn-1;mu[1]=1;phi[1]=1;for(int i=2;i<=n;i++){if(vis[i]==0) { prime[++tot]=i; phi[i]=i-1; mu[i]=-1; }for(int j=1;j<=tot && i*prime[j]<=n;j++){vis[i*prime[j]]=1;if(i%prime[j]==0){phi[i*prime[j]]=phi[i]*prime[j];break;}mu[i*prime[j]]=-mu[i];phi[i*prime[j]]=phi[i]*(prime[j]-1);}}for(int i=1;i<=n;i++) sum_mu[i]=sum_mu[i-1]+mu[i];for(int i=1;i<=n;i++) sum_phi[i]=sum_phi[i-1]+phi[i];
}
unordered_map<int,int> mp_mu;
int get_mu(int n){if(n<maxn) { return sum_mu[n]; }ll ans=0;for(int l=2,r;l<=n;l=r+1){r=n/(n/l); int d=(n/l);if(d<maxn) {  ans+=(r-l+1)*sum_mu[d]; }else           {  if(mp_mu.find(d)==mp_mu.end()) mp_mu[d]=get_mu(d); ans+=(r-l+1)*mp_mu[d]; }if(r==2147483647) break;}return mp_mu[n]=1-ans;
}
unordered_map<int,ll> mp_phi;
ll get_phi(int n){if(n<maxn) { return sum_phi[n]; }ll ans=0;for(int l=2,r;l<=n;l=r+1){r=n/(n/l); int d=(n/l);if(d<maxn) {  ans+=(r-l+1)*sum_phi[d]; }else           {  if(mp_phi.find(d)==mp_phi.end()) mp_phi[d]=get_phi(d); ans+=(r-l+1)*mp_phi[d]; }if(r==2147483647) break;}return mp_phi[n]=1ll*n*(n+1)/2-ans;
}
void work(int n){ll x=get_phi(n);int y=get_mu(n);printf("%lld %d\n",x,y);
}
int main(){get_mu_phi(); int T; scanf("%d",&T); while(T--){  int n; scanf("%d",&n); work(n); }
}

#include<bits/stdc++.h>
#define ll  long long
using namespace std;
int main(){int T; scanf("%d",&T); int tot=0;while(T--){ll n; scanf("%lld",&n);ll ans=0;for(ll l=1,r;l<=n;l=r+1){r=n/(n/l);ans+=1ll*(l+r)*(r-l+1)/2*(n/l);}//cout<<ans<<endl;//cout<<1ll*n*(n+1)/2<<endl;ans++;ans-=n;ans-=1ll*n*(n+1)/2;if(n==0) ans=0;printf("Case %d: %lld\n",++tot,ans);}
}

#include<bits/stdc++.h>
#define ll  long long
using namespace std;
const int maxn=5e6+10;
int vis[maxn];
int num[maxn];
int prime[maxn/7];
int sigma[maxn]; // yin zi he han shu
int tot=0;
int pow(int x,int n){int ans=1;while(n){if(n&1) ans=ans*x;x=x*x;n=n/2;}return ans;
}
void inint(){int n=maxn-1;vis[1]=1;sigma[1]=1;for(int i=2;i<=n;i++){//  cout<<i<<endl;if(vis[i]==0) {prime[++tot]=i; vis[i]=i; num[i]=1; sigma[i]=i+1;}for(int j=1;j<=tot&&i*prime[j]<=n;j++){vis[i*prime[j]]=prime[j];if(i%prime[j]==0){num[i*prime[j]]=num[i]+1;;sigma[i*prime[j]]=sigma[i]*(1-pow(vis[i],num[i]+1+1)) / (1-pow(vis[i],num[i]+1));break;}else {num[i*prime[j]]=1;sigma[i*prime[j]]=sigma[i]*(1+prime[j]);}}}
}
int main(){  //cout<<pow(2,5)<<endl;inint();  //cout<<sigma[4]<<endl;int tot=0;
while(1){int n; cin>>n;cout<<sigma[n]<<endl;int ans=0;for(int i=1;i<=n;i++){if(n%i==0) ans+=i;}cout<<ans<<endl;
}
}

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=5e6+10;
const int mod=1e9+7;
const int inv2=500000004;
const int inv4=250000002;
const int inv6=166666668;
bool vis[maxn];
int prime[maxn/7];
int mu[maxn];
int tot=0;
int  sum_mu[maxn];
void get_mu_phi(){int n=maxn-1;mu[1]=1;for(int i=2;i<=n;i++){if(vis[i]==0) { prime[++tot]=i;  mu[i]=-1; }for(int j=1;j<=tot && i*prime[j]<=n;j++){vis[i*prime[j]]=1;if(i%prime[j]==0){break;}mu[i*prime[j]]=-mu[i];}}for(int i=1;i<=n;i++) sum_mu[i]=sum_mu[i-1]+mu[i];
}
unordered_map<ll,ll> mp_mu;
ll get_mu(ll n){if(n<maxn) { return sum_mu[n]; }ll ans=0;for(int l=2,r;l<=n;l=r+1){r=n/(n/l);        int d=(n/l);if(d<maxn)     {  ans+=1ll*(r-l+1)*sum_mu[d]%mod; }else           {  if(mp_mu.find(d)==mp_mu.end()) mp_mu[d]=get_mu(d); ans+=1ll*(r-l+1)*mp_mu[d]%mod; }}return mp_mu[n]=(1-ans)%mod;
}
int add(int x){int ans=1ll*x*(x+1)%mod*(2*x+1)%mod*inv6%mod;ans-=1ll*3*(x+1)%mod*x%mod*inv2%mod; ans=ans%mod;ans+=1ll*2*x%mod; ans=ans%mod;return ans;
}
int make(int l,int r){  return ( add(r)-add(l-1) )%mod; }
void work(int n){ll ans=0;for(int l=1,r;l<=n;l=r+1){r=n/(n/l);  int d=n/l;if(d<maxn){ans+=1ll*make(l,r)*sum_mu[d]%mod;}else {if(mp_mu.find(d)==mp_mu.end()) mp_mu[d]=get_mu(d);ans+=1ll*make(l,r)*mp_mu[d]%mod;}}printf("%lld\n",(ans%mod+mod)%mod);
}
int main(){get_mu_phi();int T; scanf("%d",&T);while(T--){int n; scanf("%d",&n); work(n);}
}