#include <bits/stdc++.h>
#define MOD 1000000007

template<int mod>
struct ModInt{
    int x;
    ModInt():x(0){}
    ModInt(long long y):x(y>=0?y%mod:(mod-(-y)%mod)%mod){}
    ModInt &operator+=(const ModInt &p){
        if((x+=p.x)>=mod)x-=mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p){
        if((x+=mod-p.x)>=mod)x-=mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p){
        x=(int)(1LL*x*p.x%mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p){
        *this*=p.inverse();
        return *this;
    }
    ModInt operator-()const{return ModInt(-x);}
    ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
    ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
    ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
    ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
    bool operator==(const ModInt &p)const{return x==p.x;}
    bool operator!=(const ModInt &p)const{return x!=p.x;}
    explicit operator int() const { return x; }                           // added by QCFium
    ModInt operator=(const int p) {x = p; return ModInt(*this);} // added by QCFium
    ModInt inverse()const{
        int a=x,b=mod,u=1,v=0,t;
        while(b>0){
            t=a/b;
            a-=t*b;
            std::swap(a,b);
            u-=t*v;
            std::swap(u,v);
        }
        return ModInt(u);
    }
    friend std::ostream &operator<<(std::ostream &os,const ModInt<mod> &p){
        return os<<p.x;
    }
    friend std::istream &operator>>(std::istream &is,ModInt<mod> &a){
        long long x;
        is>>x;
        a=ModInt<mod>(x);
        return (is);
    }
};
typedef ModInt<MOD> mint;

int main() {
	int n;
	scanf("%d", &n);
    if (n == 1) {
		std::cout << 0 << std::endl;
		return 0;
	}
	std::vector<int> pf_table(n + 1);
	for (int i = 2; i <= n; i++)
		if (!pf_table[i]) for (int j = i; j <= n / i; j++) pf_table[j * i] = i;
	
    mint res = mint(2) * (n - 1) * (n * 2 - 1);
    for (int i = 2; i < n; i++) {
    	int so = i; int cur = i;
		while (cur > 1 && pf_table[cur]) {
			int a = pf_table[cur];
			so /= a;
			so *= a - 1;
			while (cur % a == 0) cur /= a;
		}
		if (cur > 1) {
			so /= cur;
			so *= cur-1;
		}
		res += (mint(n - i))*(mint(n) * so - mint(so) * i / 2) * 4;
    }
	std::cout << res * 2 << std::endl;
    return 0;
}