BZOJ 2671(Calc-数论反演)

#include<bits/stdc++.h>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int>
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a
<<endl;
#define PRi2D(a,n,m) For(i,n) { \
For(j,m-1) cout<<a[i][j]<<' ';\
cout<<a[i][m]<<endl; \
}
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
#define MAXN (50500+10)
typedef long long ll;
int p[MAXN],tot;
bool b[MAXN]={0};
ll mul[MAXN],s[MAXN];
void make_prime(int n)
{
tot=0; mul[1]=1;
Fork(i,2,n)
{
if (!b[i]) p[++tot]=i,mul[i]=-1;
For(j,tot)
{
if (i*p[j]>n) break;
b[i*p[j]]=1;
mul[i*p[j]]=-mul[i];
if (i%p[j]==0) {
mul[i*p[j]]=0;
break;
}
}
}
s[0]=0;
For(i,n) s[i]=s[i-1]+mul[i];
}
ll get_factor(vector<ll> &v,ll p) {
for(ll i=1;i*i<=p;i++) if (p%i==0) {
v.pb(i);
if (i*i<p) v.pb(p/i);
}
sort(v.begin(),v.end());
}
ll calc(ll n) {
ll a,b,k,ans=0,last;
vector<ll> v;
for(b=1;b*(b+1)<=n;++b) {
v.clear();
get_factor(v,b);
for(a=1;a<b&&(a+b)*b<=n;a=last+1) {
last=min(n/(n/b/(a+b))/b-b,b-1);
ll cnt=0;
for(int j=0;j<SI(v);j++) {
ll k=v[j];
cnt+=mul[k]*((last/k)-(a-1)/k);
}
ans+=n/b/(a+b)*cnt;
}
}
return ans;
}
int main()
{
//  freopen("bzoj2671.in","r",stdin);
//  freopen(".out","w",stdout);
ll n;
cin>>n;
make_prime(50000);
calc(n);
cout<<calc(n)<<endl;
return 0;
}