$$\begin{gathered} \sum _{i=1}^n\sum _{j=1}^n\varphi (gcd(i,j)) \\ \sum _{d=1}^n\varphi (d)\sum _{i=1}^n\sum _{j=1}^n[gcd(i,j)=d] \\ \sum _{d=1}^n\varphi (d)\sum _{i=1}^{\frac{n}{d}}\sum _{j=1}^{\frac{n}{d}}[gcd(i,j)=1] \\ \sum _{d=1}^n\varphi (d)\left(2\sum _{i=1}^{\frac{n}{d}}\sum _{j=1}^i[gcd(i,j)=1]-1\right) \\ \sum _{d=1}^n\varphi (d)\left(2\sum _{i=1}^{\frac{n}{d}}\varphi (i)-1\right) \end{gathered}$$

/*Author : lifehappy
*/
#include <bits/stdc++.h>using namespace std;typedef long long ll;const int N = 2e6 + 10, mod = 1e9 + 7;int prime[N], cnt, n;ll phi[N];bool st[N];void init() {phi[1] = 1;for(int i = 2; i < N; i++) {if(!st[i]) {prime[++cnt] = i;phi[i] = i - 1;}for(int j = 1; j <= cnt && 1ll * i * prime[j] < N; j++) {st[i * prime[j]] = 1;if(i % prime[j] == 0) {phi[i * prime[j]] = phi[i] * prime[j];break;}phi[i * prime[j]] = phi[i] * (prime[j] - 1);}}for(int i = 1; i < N; i++) {phi[i] = (phi[i] + phi[i - 1]) % mod;}
}unordered_map<int, ll> ans_s;ll Djs(int n) {if(n < N) return phi[n];if(ans_s.count(n)) return ans_s[n];ll ans = 1ll * n * (n + 1) / 2 % mod;for(int l = 2, r; l <= n; l = r + 1) {r = n / (n / l);ans = (ans - (r - l + 1) * Djs(n / l) % mod + mod) % mod;}return ans_s[n] = ans;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T;init();scanf("%d", &T);while(T--) {ll ans = 0;scanf("%d", &n);for(int l = 1, r; l <= n; l = r + 1) {r = n / (n / l);ans = (ans + 1ll * (Djs(r) - Djs(l - 1)) * (2ll * Djs(n / l) - 1) % mod + mod) % mod;}printf("%lld\n", ans);}return 0;
}