CF1225D

时间：2020-09-24 22:17:04 收藏：0 阅读：96

\[a_i*a_j=x^k\a_i=\prod_{i=1}^np_i^{A_i}~~~b_i=\prod_{i=1}^np_i^{B_i}~~~x=\prod_{i=1}^np_i^{C_i*k}\\prod_{i=1}^np_i^{A_i+B_i}=\prod_{i=1}^np_i^{C_i*k}\A_i+B_i=k*t~~~~~(A_i+B_i)\%k=0 \]

每一个数在质因数分解的时候记录与x相同质因数相加是k的倍数的状态为x1

用map维护每一个状态的合法总数，答案加上mp[x1],把mp[x]+1就好了

map <vector< pair<int,int> > , int > mp;
vector<pair<int,int>> x,x1; 
int n,k,a[300005];
long long ans=0;
int main() {
	scanf("%d%d",&n,&k);
	for (int i=1;i<=n;++i) {
		scanf("%d",&a[i]);
		x.clear();x1.clear();
		int aa=a[i];
		for (int j=2;j*j<=a[i];++j) {
			int tot=0;
			while(aa%j==0) {
				++tot;
				aa/=j;
				tot%=k;
			}
			if(!tot) continue;
			x.push_back({j,tot});
			x1.push_back({j,k-tot});
		}
		if(aa!=1) {
			x.push_back({aa,1});
			x1.push_back({aa,k-1});
		}
		ans=ans+mp[x1];
		++mp[x];
	}
	printf("%lld\n",ans);
}