#include <bits/stdc++.h>
using namespace std;
#define int              long long int
#define double           long double
#define print(a)         for(auto x : a) cout << x << " "; cout << endl


const int M = 1000000007;
const int N = 3e5+9;
const int INF = 2e9+1;
const int LINF = 2000000000000000001;

inline int power(int a, int b, int mod=M) {
    int x = 1;
    a %= mod;
    while (b) {
        if (b & 1) x = (x * a) % mod; 
        a = (a * a) % mod;
        b >>= 1;
    }
    return x;
}


//_ ***************************** START Below *******************************




int consistency(int n){
	int x = n;
	unordered_map<int,int> mp;
	
	while(n%2 == 0){
		mp[2]++;
		n /= 2;
	}
	
	for(int i=3; i*i<=n; i+=2){
		while(n%i==0){
			mp[i]++;
			n /= i;
		}
	}
	
	if(n>2){
		mp[n]++;
	}
	
	int ans = 1;
	for(auto& it : mp){
		int p = it.first;
		int e = it.second;
		
		int nmr = power(p, e+1, M) - 1;
		int dnr = (p-1+M)%M;
		
		dnr = power(dnr, M-2);
		
		int val = ( nmr * dnr ) % M;
		
		ans = (ans * val)%M;
		
	}
	
	ans -= x;
	
	return ans;

}










int practice(int n){


    return 0;
}





void solve() {
    
    int n;
    cin>> n;
    
    cout << consistency(n) << endl;


}





int32_t main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    int t = 1;
    cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}