#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int Lim=1500000,md=1e9+7,inv2=(md+1)/2,inv3=(md+1)/3;
ll F[4][Lim+5];
int p[Lim+5],ph[Lim+5],mu[Lim+5],v[Lim+5],T,n;
unordered_map<unsigned,ll>isval[3];
void Pre(int x){
	mu[1]=ph[1]=1;
	for(int i=2,cnt=0;i<=x;++i){
		if(!v[i]){p[++cnt]=i;mu[i]=-1;ph[i]=i-1;}
		for(int j=1,e;(e=p[j]*i)<=x&&j<=cnt;++j)
			if(!(i%p[j])){v[e]=1;ph[e]=ph[i]*p[j];break;}else v[e]=1,ph[e]=ph[i]*(p[j]-1),mu[e]=-mu[i];
	}
	for(int i=1;i<=x;++i)F[0][i]=(F[0][i-1]+ph[i])%md,F[1][i]=(F[1][i-1]+1ll*ph[i]*i)%md,F[2][i]=(F[2][i-1]+1ll*ph[i]*i%md*i)%md;
}
inline int pw1(int x){
	return 1ll*x*(x+1)/2%md;
}
inline int pw2(int x){
	return 1ll*x*(x+1)/2%md*(2ll*x+1)%md*inv3%md;
}
unordered_map<int,int> u[4];
inline int solve(unsigned int x,int type){
	if(x<=Lim)return F[type][x];
	if(u[type].find(x)!=u[type].end())return u[type][x];
	int ans=(type==0)?(pw1(x)):((type==1)?(pw2(x)):(1ll*pw1(x)*pw1(x)%md));
	for(int l=2,r;l<=(int)x;l=r+1){
		r=x/(x/l);
		int tmp=(type==0)?(r-l+1):((type==1)?(pw1(r)-pw1(l-1)):(pw2(r)-pw2(l-1))),res=solve(x/l,type);
		ans=(ans-1ll*tmp*res)%md;
	}
	return u[type][x]=(ans+md)%md;
}
int main(){
	Pre(Lim);
	while(cin>>n){
		if(!n)exit(0);
		int val0=solve(n,0),val1=solve(n,1),val2=solve(n,2),val3=solve(n/2,0),val4=solve(n/2,1),val5=solve(n/2,2);
		int S2=inv2*3ll%md,S1=inv2*((6ll*n+3)%md)%md,S0=3ll*(1ll*n*(n+1)/2%md)%md;
		int S3=S0,S4=(6ll*n+3)%md,S5=6;
		cout<<((1ll*S0*val0-1ll*S1*val1+1ll*S2*val2-1ll*S3*val3+1ll*S4*val4-1ll*S5*val5)%md+md)%md<<'\n';
	}
}