约数个数（给定数乘积的约数个数

# 题意

给定n个数，求这些数的乘积的约数的个数，答案mod 1e9+7

# 题解

累计每个数的质因子的指数，最后用指数来计算即可

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 typedef long long LL;
 4 const int mod=1e9+7;
 5 unordered_map<int,int >primes;
 6 int main(){
 7     int n;
 8     scanf("%d",&n);
 9 
10     while(n--){
11         int x;
12         scanf("%d",&x);
13         for (int i = 2; i <=x/i ; ++i)
14             while(x%i==0){
15                 x/=i;
16                 primes[i]++;
17             }
18         if(x>1) primes[x]++;
19     }
20     LL res=1;
21     for (auto prime:primes)
22         res=res*(prime.second+1)%mod;
23     cout<<res<<endl;
24     return 0;
25 }