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本文链接：https://blog.youkuaiyun.com/yusen_123/article/details/136549429

文章详细介绍了如何使用C++编写代码来计算给定整数n的欧拉函数φ(n)和莫比乌斯函数μ(n)，通过循环和模板实现高效求解，适用于数学和IT技术相关问题。

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#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<string>
#include<cstring>
#include<cmath>
#include<ctime>
#include<algorithm>
#include<utility>
#include<stack>
#include<queue>
#include<vector>
#include<set>
#include<map>
#include<unordered_map>
using namespace std;
#define LL long long
const int N = 2e6 + 10;
const long long mod = 998244353;
const double PI = acos(-1);
LL su[N], a[N], mu[N], phi[N], cn;
LL n;
map<LL, LL> mpu, mpp;
void init()
{
a[0] = a[1] = mu[1] = phi[1] = 1;
for (int i = 2; i < N; i++)
{
if (!a[i]) su[++cn] = i, mu[i] = -1, phi[i] = i - 1;
for (int j = 1; j <= cn&&(LL)i*su[j]<N; j++)
{
int pm = su[j];
a[pm * i] = 1;
if (i % pm == 0)
{
phi[i * pm] = phi[i] * pm;
break;
}
mu[i * pm] = -1 * mu[i];
phi[i * pm] = phi[i] * (pm - 1);
}
}
for (int i = 1; i < N; i++)
mu[i] += mu[i - 1], phi[i] += phi[i - 1];
}
LL seekphi(LL n)
{
if (n < N) return phi[n];
if (mpp[n]) return mpp[n];
LL ans = n * (n + 1) / 2;
for (LL l = 2, r; l <= n; l = r + 1)
{
if (n / l == 0) r = n;
else
r = min(n / (n / l),n);
ans -= (r - l + 1) * seekphi(n / l);
}
mpp[n] = ans;
return ans;
}
LL seekmu(LL n)
{
if (n < N) return mu[n];
if (mpu[n]) return mpu[n];
LL ans = 1;
for (LL l = 2, r; l <= n; l = r + 1)
{
if (n / l == 0) r = n;
else
r = min(n / (n / l), n);
ans -= (r - l + 1) * seekmu(n / l);
}
mpu[n] = ans;
return ans;
}
int main() {
init();
int T;
cin >> T;
while (T--)
{
cin >> n;
LL ans1 =seekphi(n),ans2=seekmu(n);
cout << ans1 <<" "<<ans2<< endl;
}
return 0;
}