欧拉 + 枚举
来源: https://www.acwing.com/solution/content/25752/
C++ 代码
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 1e7 + 10;
int primes[N], cnt;
bool st[N];
int phi[N];
LL s[N];
inline void init(int x)
{
for (int i = 2; i <= x; i ++ )
{
if (!st[i])
{
primes[cnt ++ ] = i;
phi[i] = i - 1;
}
for (int j = 0; primes[j] * i <= x; j ++ )
{
st[primes[j] * i] = true;
if (i % primes[j] == 0)
{
phi[primes[j] * i] = phi[i] * primes[j];
break;
}
phi[primes[j] * i] = phi[primes[j]] * phi[i];
}
}
for (int i = 1; i <= x; i ++ ) s[i] = s[i - 1] + phi[i];
}
inline void solve()
{
int n;
cin >> n;
init(n);
LL res = 0;
for (int i = 0; i < cnt; i ++ )
{
int p = primes[i];
res += (2 * s[n / p] + 1);
}
cout << res << endl;
}
int main()
{
cin.tie(nullptr) -> sync_with_stdio(0);
solve();
return 0;
}