//A tree without skin will surely die.
//A man without face is invincible.
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define sqr(x) ((x)*(x))
#define all(x) (x).begin(),(x).end()
#define Tim ((double)clock()/CLOCKS_PER_SEC)
#define mid ((l+r)>>1)
#define lowbit(x) (x&-x)
int const maxn=5e6;
int const N=maxn+10;
int const mod=1e9+7;
int const iv2=(mod+1)/2;
int n,iv6,iv4;
inline int qpow(int a,int b){
    int res=1;
    while (b){
        if (b&1) res*=a,res%=mod;
        a*=a,a%=mod,b>>=1;
    }
    return res;
}
inline int phi(int x){
    if (x==1) return 0;
    int ans=x;
    for (int i=2;i*i<=x;++i){
        if (x%i) continue;
        ans/=i,ans*=(i-1);
        while (x%i==0) x/=i;
    }
    if (x^1) ans/=x,ans*=(x-1);
    return ans%mod;
}
int cnt,pai[N],pai2[N],pai3[N],prim[N];
bool vis[N];
inline void init(){
    pai[1]=pai2[1]=pai3[1]=1;
    for (int i=2;i<=maxn;++i){
        if (!vis[i])
            prim[++cnt]=i,pai[i]=i-1,pai2[i]=pai[i]*i%mod,pai3[i]=pai2[i]*i%mod;
        for (int j=1;j<=cnt && prim[j]*i<=maxn;++j){
            vis[prim[j]*i]=1;
            if (i%prim[j]==0){
                pai[i*prim[j]]=pai[i]*prim[j]%mod;
                pai2[i*prim[j]]=pai2[i]*prim[j]%mod*prim[j]%mod;
                pai3[i*prim[j]]=pai3[i]*prim[j]%mod*prim[j]%mod*prim[j]%mod;
                break;
            }
            pai[i*prim[j]]=pai[prim[j]]*pai[i]%mod;
            pai2[i*prim[j]]=pai2[prim[j]]*pai2[i]%mod;
            pai3[i*prim[j]]=pai3[prim[j]]*pai3[i]%mod;
        }
    }
    for (int i=2;i<=maxn;++i)
        pai[i]+=pai[i-1],pai[i]%=mod,
        pai2[i]+=pai2[i-1],pai2[i]%=mod,
        pai3[i]+=pai3[i-1],pai3[i]%=mod;
}
unordered_map<int,int>ans_pai,ans_pai2,ans_pai3;
inline int smphi(int x){
    if (x<=maxn) return pai[x];
    if (ans_pai[x]) return ans_pai[x];
    int ans=x*(x+1)%mod*iv2%mod;
    for (int l=2,r;l<=x;l=r+1){
        r=x/(x/l);
        ans+=mod-((r-l+1)*smphi(x/l)%mod),ans%=mod;
    }
    return ans_pai[x]=ans;
}
inline int smphi1(int x){
    if (x<=maxn) return pai2[x];
    if (ans_pai2[x]) return ans_pai2[x];
    int ans=(x+1)*x%mod*(2*x+1)%mod*iv6%mod;
    for (int l=2,r;l<=x;l=r+1){
        r=x/(x/l);
        ans+=mod-(((l+r)*(r-l+1)/2)%mod*smphi1(x/l)%mod),ans%=mod;
    }
    return ans_pai2[x]=ans;
}
inline int qr(int x){
    return (x+1)*x%mod*(2*x%mod+1)%mod*iv6%mod;
}
inline int smphi2(int x){
    if (x<=maxn) return pai3[x];
    if (ans_pai3[x]) return ans_pai3[x];
    int ans=x*x%mod*(x+1)%mod*(x+1)%mod*iv4%mod;
    for (int l=2,r;l<=x;l=r+1){
        r=x/(x/l);
        ans+=mod-((qr(r)+mod-qr(l-1))%mod*smphi2(x/l)%mod),ans%=mod;
    }
    return ans_pai3[x]=ans;
}
inline int qzphi0(int x){
    if (x==0) return 0;
    return smphi(x)-1;
}
inline int qzphi1(int x){
    if (x==0) return 0;
    return smphi1(x)-1;
}
inline int qzphi2(int x){
    if (x==0) return 0;
    return smphi2(x)-1;
}
void solve(){
    while (cin>>n){
        int ans=2*n-2;
        int nt=qzphi2(n-1),no=qzphi1(n-1),nz=qzphi0(n-1);
        int gt=qzphi2(n/2),go=qzphi1(n/2),gz=qzphi0(n/2);
        nt-=gt,no-=go,nz-=gz;
        ans+=((n*n+n)%mod*nz%mod-(2*n+1)*no%mod+nt)%mod*iv2%mod;
        ans+=((2*n+1)%mod*go%mod-3*gt%mod)*iv2%mod;
        nt=qzphi2(n),no=qzphi1(n),nz=qzphi0(n);
        ans+=((n*n+n)%mod*nz%mod-(2*n+1)*no%mod+nt)%mod;
        ans-=((n*n+n)%mod*gz%mod-(2+4*n)%mod*go%mod+4*gt%mod)%mod;
        ans+=(n*(n-1)/2)%mod;
        if (n/2>=1) ans-=((n-1)*(n-2)/2)%mod;
        ans%=mod,ans+=mod,ans%=mod;
        cout<<ans<<'\n';
    }
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0),cout.tie(0);
    int t=1;init();
    iv6=qpow(6,mod-2);
    iv4=qpow(4,mod-2);
    // cin>>t;
    while (t--) solve();
    return 0;
}