The only decomposition theorem entry

Unique Factorization Theorem : a positive integer greater than 1 for each of the product can be decomposed into a finite number of prime numbers, if prime factor excluding the product in order, the decompositions are unique. The prime factorization of n same prime factor collected together, may only be a positive integer n greater than 1 each may be uniquely written as P = n ₁ ^A1 P ₂ ^A2 P _{. 3} ^A3 ... P _K ^AK ,wherein, p1,P2, P . 3, ..., PK  , are mutually different prime numbers, and a1, a2, a3, ..., ak is a positive integer, above referred to as n-type decomposition of the canonical decomposition.

Properties: The number n of the divisor n, τ (n) = (1 + a1) (1 + a2) (1 + a3) ...... (1 + ak); n is the number of positive and about, [sigma] (n-) = (. 1 P1 + P1 + ... + ^A1 ) (. 1 P2 + P2 + ... + ^A2 ) ... (. 1 + PK + ... + PK ^AK )

 Template code:

 1 /* */
 2 #include <iostream>
 3 #include <cstdio>
 4 #include <cstring>
 5 #include <string>
 6 #include <cmath>
 7 #include <algorithm>
 8 using namespace std;
 9 typedef long long ll;
10 const int maxn=1e5;
11 bool is[maxn];
12 int cnt=0;
13 ll a[maxn];//存素数
14DS LL [MAXN], ZS [MAXN]; // DS is the base, ZS is the index 
15  
16  void the init () // play table, Euler sieve 
. 17  {
 18 is      Memset ( IS , to true , the sizeof ( IS ));
 . 19      IS [ 0 ] = IS [ . 1 ] = to false ;
 20 is      for ( int I = 2 ; I <MAXN; I ++ )
 21 is      {
 22 is          IF ( IS [I]) A [CNT ++] = I;
 23 is          for (int j=0; i*a[j]<maxn&&j<cnt; j++)
24         {
25             is[i*a[j]]=false;
26             if( i%a[j]==0 ) break;
27         }
28     }
29 }
30 
31 ll fj(ll x)//不同素数的个数
32 {
33     ll k=0,flag=0;
34     for(ll i=0; i<cnt; i++ )
35     {
36         while(x%a[i]==0)
37         {
38             if(flag==0)
39             {
40                 flag=1;
41                 k++;
42             }
43             x/=a[i];
44             ds[k]=a[i];
45             zs[k]++;
46         }
47         if(x==1) break;
48         flag=0;
49     }
50     if(! X = 1 ) // If exploded End x are not equal to 1, then x must be a prime number 
51 is      {
 52 is          K ++ ;
 53 is          DS [K] = x;
 54 is          ZS [K] = 1 ;
 55      }
 56 is      return K;
 57 is  }
 58  
59  int main ()
 60  {
 61 is      the init ();
 62 is      LL X;
 63 is      CIN >> X;
 64      LL K = FJ (X);
 65      for (LL I = . 1 ; I <= K; I ++) the printf ( " % c% LLD LLD ^%",ds[i],zs[i],i==k?'\n':'+');
66     return 0;
67 }