//#pragma GCC optimize ("O3")
//#pragma GCC target ("avx")
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define rep1(i, n) for(int i = 1; i <= (n); i++)
#define co(x) cout << (x) << "\n"
#define cosp(x) cout << (x) << " "
#define ce(x) cerr << (x) << "\n"
#define cesp(x) cerr << (x) << " "
#define pb push_back
#define mp make_pair
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define Would
#define you
#define please

const int mod = 1e9 + 7;
ll modpow(ll A, ll B) {
	ll kotae = 1;
	while (B > 0) {
		if (B & 1) kotae = kotae * A % mod;
		A = A * A % mod;
		B >>= 1;
	}
	return kotae;
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);


	int N, K;
	cin >> K;
	N = 3;

	ll kosuu[100001] = {};
	for (int i = K; i >= 1; i--) {
		int k = K / i;
		ll tmp = modpow(k, N);
		for (int j = i + i; j <= K; j += i) {
			tmp -= kosuu[j];
		}
		kosuu[i] = (tmp % mod + mod) % mod;
	}
	ll kotae = 0;
	rep1(i, K) {
		kotae += kosuu[i] * i % mod;
	}
	co(kotae% mod);

	Would you please return 0;
}