python/TangDou/Topic/Mobius/P4318.cpp

#include <bits/stdc++.h>
using namespace std;
const int N = 100010;

// 筛法求莫比乌斯函数(枚举约数)
int mu[N], sum[N]; // sum[N]:梅滕斯函数,也就是莫比乌斯函数的前缀和
int primes[N], cnt;
bool st[N];
void get_mobius(int n) {
    mu[1] = 1;
    for (int i = 2; i <= n; i++) {
        if (!st[i]) {
            primes[cnt++] = i;
            mu[i] = -1;
        }
        for (int j = 0; primes[j] <= n / i; j++) {
            int t = primes[j] * i;
            st[t] = true;
            if (i % primes[j] == 0) {
                mu[t] = 0;
                break;
            }
            mu[t] = -mu[i];
        }
    }
    // 维护u(x)前缀和:梅滕斯函数
    for (int i = 1; i <= n; i++) sum[i] = sum[i - 1] + mu[i];
}
long long check(long long g) {
    long long res = 0;
    for (int i = 1; i * i <= g; i++)
        res = res + mu[i] * (g / i / i);

    return res;
}

int main() {
    get_mobius(N - 1);

    int t, k;
    cin >> t;
    while (t--) {
        cin >> k;
        long long l = 1, r = 2e9, mid, vt;
        while (l <= r) {
            mid = (l + r) / 2;
            vt = check(mid);
            if (vt < k)
                l = mid + 1;
            else
                r = mid - 1;
        }
        cout << r + 1 << endl;
    }
    return 0;
}