'commit'

TangDou/Topic/Mobius/SQP4168.cpp

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+#include <iostream>
+#include <cstdio>
+#include <cmath>
+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;
+    }
+}

TangDou/Topic/Mobius/SQP4168.in

@@ -0,0 +1,4 @@
+3
+1
+1000
+100000000000000