python/TangDou/Topic/Mobius/P4318.cpp

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define endl "\n"
const int N = 100010;

// 筛法求莫比乌斯函数(枚举约数)
int mu[N];
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];
        }
    }
}
int check(int mid, int k) {
    int res = 0;
    for (int i = 1; i * i <= mid; i++) // 枚举范围内每个平方数
        res += mu[i] * (mid / i / i);
    return res >= k;
}

signed main() {
    // 获取莫比乌斯函数值
    get_mobius(N - 1);

    int T, k;
    cin >> T; // T组测试数据
    while (T--) {
        cin >> k; // 第k个数
        int l = 1, r = 2e9;
        while (l < r) {
            int mid = l + r >> 1;
            if (check(mid, k))
                r = mid;
            else
                l = mid + 1;
        }
        cout << r << endl;
    }
}