【模板】杜教筛（Sum）

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\(\text{Code}\)

#include<cstdio>
#include<tr1/unordered_map>
#define LL long long
using namespace std;
const int M = 5e6;
int vis[M + 5],p[M + 5],tot,T,n;
LL phi[M + 1],mu[M + 1];

tr1::unordered_map<int,LL> fm,fp;
void init()
{
	mu[1] = phi[1] = 1LL;
	for (int i = 2; i <= M; i++)
	{
		if (!vis[i]) p[++tot] = i,mu[i] = -1,phi[i] = i - 1;
		for (int j = 1; j <= tot && p[j] * i <= M; j++)
		{
			vis[p[j] * i] = 1;
			if (i % p[j] == 0) {phi[i * p[j]] = phi[i] * p[j]; break;}
			mu[p[j] * i] = -mu[i],phi[i * p[j]] = phi[i] * phi[p[j]];
		}
	}
	for (int i = 1; i <= M; i++) mu[i] += mu[i - 1],phi[i] += phi[i - 1];
}
LL getmu(int x)
{
	if (x <= M) return mu[x];
	if (fm[x]) return fm[x];
	LL res = 1LL;
	for (LL l = 2,r; l <= x; l = r + 1)
		r = x / (x / l),res -= (LL)(r - l + 1) * getmu(x / l);
	return fm[x] = res;
}
LL getp(int x)
{
	if (x <= M) return phi[x];
	if (fp[x]) return fp[x];
	LL res = (LL)x * (x + 1LL) / 2;
	for (LL l = 2,r; l <= x; l = r + 1)
		r = x / (x / l),res -= (LL)(r - l + 1) * getp(x / l);
	return fp[x] = res;
}
int main()
{
	init(),scanf("%d",&T);
	for (; T; T--) scanf("%d",&n),printf("%lld %lld\n",getp(n),getmu(n));
}

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