#include <atcoder/all>
using namespace atcoder;
#include <bits/stdc++.h>
using namespace std;
// #include <boost/multiprecision/cpp_int.hpp>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep2(i,a,b) for (int i = (int)(a); i < (int)(b); i++)
#define all(v) v.begin(),v.end()
#define inc(x,l,r) ((l)<=(x)&&(x)<(r)) 
#define Unique(x) sort(all(x)), x.erase(unique(all(x)), x.end())
#define pcnt __builtin_popcountll
typedef long long ll;
#define int ll
using ld = long double;
using vi = vector<int>;
using vs = vector<string>;
using P = pair<int,int>;
using vp = vector<P>;
// using Bint = boost::multiprecision::cpp_int;
template<typename T1,typename T2> bool chmax(T1 &a, const T2 b) {if (a < b) {a = b; return true;} else return false; }
template<typename T1,typename T2> bool chmin(T1 &a, const T2 b) {if (a > b) {a = b; return true;} else return false; }
template<typename T> using priority_queue_greater = priority_queue<T, vector<T>, greater<T>>;
template<typename T> ostream &operator<<(ostream &os,const vector<T> &v){rep(i,v.size())os<<v[i]<<(i+1!=v.size()?" ":"");return os;}
template<typename T> istream &operator>>(istream& is,vector<T> &v){for(T &in:v)is>>in;return is;}
template<typename T1,typename T2> ostream &operator<< (ostream &os, const pair<T1,T2> &p){os << p.first <<" "<<p.second;return os;}
ostream &operator<< (ostream &os, const modint1000000007 &m){os << m.val();return os;}
istream &operator>> (istream &is, modint1000000007 &m){ll in;is>>in;m=in;return is;}
ostream &operator<< (ostream &os, const modint998244353 &m){os << m.val();return os;}
istream &operator>> (istream &is, modint998244353 &m){ll in;is>>in;m=in;return is;}
template<class... T> void input(T&... a){(cin>> ... >> a);}
template<class T> void print(T& a){cout <<a<< '\n';}
template<class T,class... Ts> void print(const T&a, const Ts&... b){cout<< a;(cout<<...<<(cout<<' ',b));cout<<'\n';}
#define VI(v,n) vi v(n); input(v)
#define INT(...) int __VA_ARGS__; input(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; input(__VA_ARGS__)
#define CHAR(...) char __VA_ARGS__; input(__VA_ARGS__)
int sign(ll x){return x>0?1:x<0?-1:0;}
ll ceil(ll x,ll y){assert(y!=0);if(sign(x)==sign(y))return (x+y-1)/y;return -((-x/y));}
ll floor(ll x,ll y){assert(y!=0);if(sign(x)==sign(y))return x/y;if(y<0)x*=-1,y*=-1;return x/y-(x%y<0);}
ll abs(ll x,ll y){return abs(x-y);}
ll bit(int n){return 1ll<<n;}
bool ins(string s,string t){return s.find(t)!=string::npos;}
P operator+ (const P &p, const P &q){ return P{p.first+q.first,p.second+q.second};}
P operator- (const P &p, const P &q){ return P{p.first-q.first,p.second-q.second};}
void yesno(bool ok,string y="Yes",string n="No"){ cout<<(ok?y:n)<<endl;}
void YESNO(bool ok,string y="YES",string n="NO"){ cout<<(ok?y:n)<<endl;}
int di[]={-1,0,1,0,-1,-1,1,1};
int dj[]={0,1,0,-1,-1,1,-1,1};
const ll INF = 8e18;
//using mint = modint1000000007;
//using mint = modint998244353;
//mint stom(const string &s,int b=10){mint res = 0;for(auto c:s)res *= b,res += c-'0';return res;}
vector<int> f_(10000001,-1),g_(10000001,-1);
P fg(int n){
    if(n==0)return {-1,-1};
    if(f_[n]!=-1)return {f_[n],g_[n]};
    int cf = 2,cg = 2,j = 2;
    int k1 = n/j;
    while(k1>1){
        int j2 = n/k1+1;
        auto [ff,gg] = fg(k1);
        cf += (j2-j)*(2*ff+1);
        cg += (j2-j)*(k1*(k1-1)+1-2*gg);
        j = j2;
        k1 = n/j2;
    }
    f_[n]=(n*(n-1)-cf+j)/2;
    g_[n]=(cg-j)/2;
    return {f_[n],g_[n]};
}
int g(int n){
    if(n==0)return 0;
    if(g_[n]!=-1)return g_[n];
    int c = 2,j = 2;
    int k1 = n/j;
    while(k1>1){
        int j2 = n/k1+1;
        c += (j2-j)*(k1*(k1-1)+1-2*(g(k1)));
        j = j2;
        k1 = n/j2;
    }
    return g_[n]=(c-j)/2;
}
void naive(int n){
    int G[n][n];
    rep(i,n)rep(j,n)G[i][j]=gcd(i+1,j+1);
    rep(i,n)G[i][i]=0;
    rep(k,n)rep(i,n)rep(j,n)chmin(G[i][j],G[i][k]+G[k][j]);
    int res = 0;
    vi cnt(3);
    rep(i,n)rep(j,i){
        res+=G[i][j];
        cnt[G[i][j]]++;
    }
    // rep(i,n)for(int j=i+1;j<n;j++)cout<<G[i][j]<<" \n"[j==n-1];
    print(n,cnt[2],g(n));
}

signed main() {
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);

    // for(int n=2;n<=100;n++)naive(n);
    INT(t);
    while(t--){
        INT(n);
        auto [f,g] = fg(n);
        print(f+2*g);
    }
    return 0;
}