#include using namespace std; #define int long long #define endl "\n" const int M = 110, N = 10000010; int t, m, sqrtN, n, ans, q[M]; // 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]; } signed main() { #ifndef ONLINE_JUDGE freopen("SQP4168.in", "r", stdin); #endif cin >> t; for (int i = 1; i <= t; i++) { cin >> q[i]; n = max(n, q[i]); } sqrtN = sqrt(n); get_mobius(sqrtN); // 线性求莫比乌斯函数, 前缀和 for (int i = 1; i <= t; i++) { n = q[i]; ans = 0; for (int l = 1, r; l <= n; l = r + 1) { if (n / (l * l) == 0) { break; } r = sqrt(n / (n / (l * l))); ans += n / (l * l) * (sum[r] - sum[l - 1]); } printf("%lld\n", ans); } }