luogu P2424 约数和 |数论分块

把\(f(x)\)用数学方式表示一下就是\(f(x)=\sum\limits_{d|x}d\)

那 \(ans=\sum\limits_{i=x}^{y}f(i)=\sum\limits_{i=x}^{y}\sum\limits_{d|i}d\)

经典数论分块

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
const int N=1e6+5;
#define int long long
int sum(int n) {
    if(n<=1) return n;
    int ans=0;
    for(int l=1,r;l<=n;l=r+1) {
        r=n/(n/l);
        ans+=(n/l)*(l+r)*(r-l+1)/2;
    }
    return ans;
}
int n,m;
signed main(){
	cin>>n>>m;
	printf("%lld\n",sum(m)-sum(n-1));
}