BZOJ 2440: [中山市选2011]完全平方数

二分,然后用莫比乌斯做就行了...

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;

const int maxn = 50005;

int not_prime[maxn];
int prime[maxn];
int mu[maxn];
int K, p_cnt;

void Init()
{
	mu[1] = 1;
	p_cnt = 0;
	for(int i = 2; i < maxn; i++) {
		if(!not_prime[i]) {
			prime[p_cnt++] = i;
			mu[i] = -1;
		}
		for(int j = 0; j < p_cnt && i * prime[j] < maxn; j++) {
			not_prime[i * prime[j]] = 1;
			if(i % prime[j]) mu[i * prime[j]] = -mu[i];
			else {
				mu[i * prime[j]] = 0;
				break;
			}
		}
	}
}

bool check(LL x)
{
	int tt = sqrt(x);
	LL res = 0;
	for(LL i = 1; i <= tt; i++) {
		res += mu[i] * (x / (i * i));
	}
	return res >= K;
}

void work()
{
	scanf("%d", &K);
	
	LL top = 2e9, bot = 1, mid, res;
	
	while(top >= bot) {
		mid = (bot + top) >> 1;
		if(check(mid)) res = mid, top = mid - 1;
		else bot = mid + 1;
	}
	printf("%lld\n", res);
}

int main()
{
	//freopen("data", "r", stdin);
	Init();
	int _;
	scanf("%d", &_);
	while(_--) work();
	
	return 0;
}