Count Divisors of Factorial

//https://practice.geeksforgeeks.org/problems/count-divisors-of-factorial/0?fbclid=IwAR3RsG4Ad7Z-g8RtxBos7BFT7fdUucqy5ByUiG26_CRZPwQnQHO9hVZ5g28

#include <bits/stdc++.h>
using namespace std;
typedef long long ll  ; 
//Silver_Lining 
void PrimeFactor ( ll n , vector < ll > &v )
{
    ll arr [ n + 1 ] ; 
    memset ( arr , 0 , sizeof ( arr ) ) ; 
    for ( ll i = 2 ; i <= n ; i ++ )
    {
        if ( arr [ i ] == 0 )
        {
            v.push_back ( i ) ; 
            ll k = 2 ; 
            while ( i * k <=  n )
            {
                arr [ i * k ]  = 1 ;  
                k ++ ; 
            }
        }
    }
}
ll Lagendre ( ll n , ll prime  ) 
{
    ll c = 0 ; 
    while ( n > 0 )
    {
        n = n / prime ; 
        c += n ; 
    }
    
    return c ; 
}
int main() {
    
    
    ll T ; 
    cin >> T ; 
    while ( T-- )
    {
        ll n , ans = 1 ; 
        cin >> n ; 
        vector < ll > prime ;
        PrimeFactor (  n , prime  ) ; 
       /* for ( ll i = 0 ; i < prime.size() ;  i ++ )
            cout << prime [ i ] << " " ; 
        cout << endl ;*/ 
        for ( ll i = 0 ; i <  prime.size() ; i ++ )
        {
            ll c = Lagendre ( n , prime [ i ] ) + 1 ; 
            ans = ans  *  c ; 
        }
        
        cout << ans << endl ; ; 
        
    }
	//code
	return 0;
}