（洛谷P4213）杜教筛

https://www.cnblogs.com/Mychael/p/8744633.html

#pragma GCC optimize(3, "Ofast", "inline")

#include <bits/stdc++.h>

#define start ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define ll long long
//#define int ll
#define ls st<<1
#define rs st<<1|1
using namespace std;
const int maxn = (ll) 5e6 + 5;
const int mod = 1000000007;
const int inf = 0x3f3f3f3f;
int mu[maxn];
ll phi[maxn];
bool vis[maxn];
int v[maxn];

inline void init() {
    int cnt = 0;
    mu[1] = phi[1] = 1;
    for (int i = 2; i < maxn; ++i) {
        if (!vis[i]) {
            v[++cnt] = i;
            mu[i] = -1;
            phi[i] = i - 1;
        }
        for (int t = 1; t <= cnt && i * v[t] < maxn; ++t) {
            int j = v[t];
            vis[i * j] = true;
            if (i % j) {
                mu[i * j] = -mu[i];
                phi[i * j] = phi[i] * phi[j];
            } else {
                mu[i * j] = 0;
                phi[i * j] = phi[i] * j;
                break;
            }
        }
    }
    for (int i = 1; i < maxn; ++i) {
        mu[i] += mu[i - 1];
        phi[i] += phi[i - 1];
    }
}

unordered_map<int, ll>  ansphi;
unordered_map<int, ll>  ansmu;

inline int getmu(int n) {
    if (n < maxn)
        return mu[n];
    if (ansmu[n])
        return ansmu[n];
    int ans = 1;
    for (unsigned int l = 2, r; l <= n; l = r + 1) {
        r = n / (n / l);
        ans -= (r - l + 1) * getmu(n / l);
    }
    return ansmu[n] = ans;
}

inline ll getphi(int n) {
    if (n < maxn)
        return phi[n];
    if (ansphi[n])
        return ansphi[n];
    ll ans = 1ll*n * (n + 1) / 2;
    for (unsigned int l = 2, r; l <= n; l = r + 1) {
        r = n / (n / l);
        ans -= (r - l + 1) * getphi(n / l);
    }
    return ansphi[n] = ans;
}

signed main() {
    start;
    init();
    int T;
    cin >> T;
    while (T--) {
        int n;
        cin >> n;
        cout << getphi(n) << ' ' << getmu(n) << '\n';
    }
    return 0;
}