线性筛 [约数个数/约数和]

博客1
因子个数

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
#include<cstdlib>
#include<cmath>
#include<stack>
#include<map>
#include<vector>
#include<algorithm>
using namespace std;
#define ll long long
#define lb long double
#define INF 0x3f3f3f3f
#define maxn 3000025
bool prime[maxn];
int cnt;
ll Prime[maxn], num[maxn], mini[maxn];
void make_(){
    memset(prime, true, sizeof(prime));
    prime[0] = prime[1] = false;
    num[1] = 1;
    for(int i = 2 ; i < maxn ; ++ i){
        if(prime[i]){
            Prime[++cnt] = i;
            num[i] = 2;
            mini[i] = 1;
        }
        for(int j = 1 ; j <= cnt && i * Prime[j] < maxn ; ++ j){
            prime[i * Prime[j]] = false;
            if(i % Prime[j] == 0){
                mini[i * Prime[j]] = num[i] + 1;
                num[i * Prime[j]] = num[i] / (1 + mini[i]) * (1 + mini[i * Prime[j]]);
            }
            else{
                num[i * Prime[j]] = num[i] * num[Prime[j]];
                mini[i * Prime[j]] = 1;
            }
        }
    }
}
int main()
{
    make_();
    return 0;
}

因子和

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
#include<cstdlib>
#include<cmath>
#include<stack>
#include<map>
#include<vector>
#include<algorithm>
using namespace std;
#define ll long long
#define lb long double
#define INF 0x3f3f3f3f
#define maxn 3000025
bool prime[maxn];
int cnt;
ll Prime[maxn], num[maxn], mini[maxn];
void make_(){
    memset(prime, true, sizeof(prime));
    prime[0] = prime[1] = false;
    num[1] = 1;
    for(int i = 2 ; i < maxn ; ++ i){
        if(prime[i]){
            Prime[++cnt] = i;
            num[i] = 1 + i;
            mini[i] = 1 + i;
        }
        for(int j = 1 ; j <= cnt && i * Prime[j] < maxn ; ++ j){
            prime[i * Prime[j]] = false;
            if(i % Prime[j] == 0){
                mini[i * Prime[j]] = num[i] * Prime[j] + 1;
                num[i * Prime[j]] = num[i] / mini[i] * mini[i * Prime[j]];
            }
            else{
                num[i * Prime[j]] = num[i] * num[Prime[j]];
                mini[i * Prime[j]] = 1 + Prime[j];
            }
        }
    }
}
int main()
{
    make_();
    return 0;
}