A prime number p≥2 is an integer which is evenly divisible by only two integers: 1 and p. A composite integer is one which is not prime. The fundamental theorem of arithmetic says that any integer x can be expressed uniquely as a set of prime factors – those prime numbers which, when multiplied together, give x. Consider the prime factorization of the following numbers:
10=2×5 16=2×2×2×2 231=3×7×11
Consider the following process, which we’ll call prime reduction. Given an input x:

if xx is prime, print xx and stop
factor xx into its prime factors p1,p2,…,pk
let x=p1+p2+?+pk
go back to step 1
Write a program that implements prime reduction.

Input
Input consists of a sequence of up to 2000020000 integers, one per line, in the range 22 to 109109. The number 44 will not be included in the sequence (try it to see why it’s excluded). Input ends with a line containing only the number 4.

Output
For each integer, print the value produced by prime reduction executed on that input, followed by the number of times the first line of the process executed.

2
3
5
76
100
2001
4

2 1
3 1
5 1
23 2
5 5
5 6

大意就是：给你一个数x——1、如果x是素数，直接输出x以及循环的步数。2、如果不是，那就x分解质因数，把所有质因数之和给x，步数+1，执行第一步。

 //Asimple
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n, m, s, res, ans, len, T, k, num;

bool is_pr(ll n) {
    for(int i=2; i*i<=n; i++) {
        if( n%i==0 ) return false;
    }
    return true;
}

ll solve(ll n){
    ll ans = 0;
    int i = 2;
    while( n>1 ) {
        if( n%i==0 ) {
            ans += i;
            n /= i;
            if( is_pr(n) ) {//这步是关键，不写超时
                ans += n;
                break;
            } 
        } else ++i;
    }
    return ans;
} 

void input() {
    while( cin >> n) {
        res = 1;
        if( n == 4 ) break;
        while( !is_pr(n) ) {
            n = solve(n);
            res ++;
        }
        cout << n << " " << res << endl;
    }
}

int main(){
    input();
    return 0;
}

Kattis之旅——Prime Reduction