#include #include #include using namespace std; #define int long long #define endl "\n" const int N = 1e7 + 10; // 枚举到sqrt(1e14)=1e7即可 // 筛法求莫比乌斯函数(枚举约数) int mu[N], s1[N], s2[N]; // s1[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++) s1[i] = s1[i - 1] + mu[i]; for (int i = 1; i <= n; i++) s2[i] = s2[i - 1] + mu[i] * mu[i]; } int calc(int n) { if (n <= N) return s2[n]; int res = 0, m = sqrt(n); for (int l = 1, r; l <= m; l = r + 1) { r = min((int)sqrt(n / (n / (l * l))), m); res += (n / (l * l)) * (s1[r] - s1[l - 1]); } return res; } signed main() { #ifndef ONLINE_JUDGE freopen("SQP4168.in", "r", stdin); /* 1 608 60792710185947 */ #endif int n, T; cin >> T; get_mobius(N - 1); while (T--) { cin >> n; cout << calc(n) << endl; } }