约数之和

 1 #include <iostream>
 2 #include <cstring>
 3 #include <cstdio>
 4 #include <algorithm>
 5 #include <unordered_map>
 6 
 7 using namespace std;
 8 
 9 typedef long long LL;
10 typedef unordered_map<int, int> unmap;
11 
12 const int mod = 1e9 + 7;
13 
14 unmap prime;
15 
16 int main() 
17 {
18     int n;
19     scanf("%d", &n);
20     while (n -- ) 
21     {
22         int x;
23         scanf("%d", &x);
24 
25         for (int i = 2; i <= x / i; i ++ )
26             while (x % i == 0) 
27             {
28                 x /= i;
29                 prime[i] ++ ;
30             }
31 
32         if (x > 1) prime[x] ++ ;
33     }
34 
35     LL res = 1;
36 
37     for (unmap::iterator it = prime.begin(); it != prime.end(); it ++ ) 
38     {
39         LL sum = 1;
40         LL cnt = 1;
41         for (int i = 1; i <= it -> second; i ++ )
42         {
43             cnt = cnt * it -> first % mod;
44             sum = (sum + cnt) % mod;
45         }
46         res = res * sum % mod;
47     }
48 
49     printf("%lld", res);
50 
51     return 0;
52 }