[欧拉函数] BZOJ 2226 [Spoj 5971] LCMSum

来源：互联网发布：linux编译工具链编辑：程序博客网时间：2024/04/19 09:35

显然ans=Σ[d|n]d*F(n/d)/d=nΣF(d)

F(n)为n以内与n互质的数之和

F(n)=n*phi(n)/2 由互质的对称性[ gcd(i,n)==1 <=> gcd(n-i,n) ] 可知

#include<cstdio>#include<cstdlib>#include<algorithm>#include<cmath>using namespace std;typedef long long ll;inline char nc(){static char buf[100000],*p1=buf,*p2=buf;if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }return *p1++;}inline void read(int &x){char c=nc(),b=1;for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;}const int maxn=1000000;int prime[maxn+5],num;int phi[maxn+5];int vst[maxn+5];inline void Pre(){phi[1]=1;for (int i=2;i<=maxn;i++){if (!vst[i])prime[++num]=i,phi[i]=i-1;for (int j=1;i*prime[j]<=maxn;j++){vst[i*prime[j]]=1;if (i%prime[j]==0){phi[i*prime[j]]=prime[j]*phi[i];break;}elsephi[i*prime[j]]=phi[i]*phi[prime[j]];}}}inline ll F(int i){if (i==1) return 1LL;return (ll)phi[i]*i>>1;}int main(){ll ret=0;int n,Q;freopen("t.in","r",stdin);freopen("t.out","w",stdout);Pre();read(Q);while (Q--){ret=0;read(n);int i;for (i=1;i*i<n;i++)if (n%i==0)ret+=F(i),ret+=F(n/i);if (i*i==n)ret+=F(i);printf("%lld\n",ret*n);}return 0;}

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