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58 lines
1.4 KiB
58 lines
1.4 KiB
#include <bits/stdc++.h>
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using namespace std;
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#define int long long
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#define endl "\n"
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const int M = 110, N = 10000010;
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int t, m, sqrtN, n, ans, q[M];
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// 筛法求莫比乌斯函数(枚举约数)
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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
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int primes[N], cnt;
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bool st[N];
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void get_mobius(int n) {
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mu[1] = 1;
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for (int i = 2; i <= n; i++) {
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if (!st[i]) {
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primes[cnt++] = i;
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mu[i] = -1;
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}
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for (int j = 0; primes[j] <= n / i; j++) {
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int t = primes[j] * i;
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st[t] = true;
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if (i % primes[j] == 0) {
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mu[t] = 0;
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break;
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}
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mu[t] = -mu[i];
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}
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}
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// 维护u(x)前缀和:梅滕斯函数
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for (int i = 1; i <= n; i++) sum[i] = sum[i - 1] + mu[i];
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}
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signed main() {
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#ifndef ONLINE_JUDGE
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freopen("SQP4168.in", "r", stdin);
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#endif
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cin >> t;
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for (int i = 1; i <= t; i++) {
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cin >> q[i];
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n = max(n, q[i]);
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}
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sqrtN = sqrt(n);
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get_mobius(sqrtN); // 线性求莫比乌斯函数, 前缀和
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for (int i = 1; i <= t; i++) {
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n = q[i];
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ans = 0;
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for (int l = 1, r; l <= n; l = r + 1) {
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if (n / (l * l) == 0) { break; }
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r = sqrt(n / (n / (l * l)));
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ans += n / (l * l) * (sum[r] - sum[l - 1]);
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}
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printf("%lld\n", ans);
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}
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} |