P2398 GCD SUM

https://www.luogu.com.cn/record/80288917

Luogu/P2398/P2398.cpp

@@ -0,0 +1,42 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+
+int n, phi[N];
+long long sum[N], ans;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    phi[1] = 1;
+    for (int i = 2; i <= n; i++) {
+        phi[i] = i;
+    }
+
+    for (int i = 2; i <= n; i++) {
+        if (phi[i] == i) {
+            for (int j = i; j < N; j += i) {
+                phi[j] = phi[j] / i * (i - 1);
+            }
+        }
+    }
+
+    for (int i = 1; i <= n; i++) {
+        sum[i] = sum[i - 1] + phi[i];
+    }
+
+    for (int i = 1; i <= n; i++) {
+        ans += (sum[n / i] * 2 - 1) * i;
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}