Number Of Divisors (NOD)

Number of Divisors(NOD)

Given N you have to find the number of divisors of N.

Solution:
Step 1: Generating Prime using Sieve of Eratosthenes
Step 2: Count Divisors using prime factorization

CODE:

long long NOD_using_factorization( long long n )           /// O(lof2(N))
{
    long long  sqrtn = sqrt ( n );
    long long tmp = 1,divisors = 1;
    for ( int i = 0; i < prime.size() && prime[i] <= sqrtn; i++ )
    {
        ///if ( sieve[n] == 0 ) break; ///*Checks if n is prime or not*/ Please comment This line if n > 1e7
        if ( n % prime[i] == 0 )
        {
            tmp = 1;
            while ( n % prime[i] == 0 )
            {
                n /= prime[i];
                tmp++;
            }
            divisors *=tmp;
            sqrtn = sqrt ( n );
        }
    }
    if ( n != 1 )
    {
        divisors*=2;
    }
    return divisors;
}