Primen't Divisors

Yuhao and William are both great friends. One day, Yuhao told William about prime numbers but William got annoyed after knowing that prime numbers do not have any divisor except 1 and itself. William only likes non-prime numbers. To appease William, Yuhao decided to give William a problem:

Given a number $N$, find the number of its non-prime divisors.

Example:

Input:  n = 4
Output: 2

Approach

C++

#include <bits/stdc++.h>

using namespace std;
int main()
{
    int N = 100000, prime[100001] = {0}, v[100001];
    prime[2] = 1;
    for (long long int i = 3; i <= N; i += 2)
        prime[i] = 1;
    v[0] = 2;
    long long int k = 1;
    for (long long int i = 3; i <= N; i += 2)
    {
        if (prime[i])
        {
            v[k] = i;
            k++;
            for (long long int j = i * i; j <= N; j += 2 * i)
                prime[j] = 0;
        }
    }

    long long int n = 4;
    long long int i = 0, p1 = v[0], ans = 1, d = 0;
    while (p1 * p1 <= n && i < k)
    {
        long long int c = 0;
        while (n % p1 == 0)
        {
            n = n / p1;
            c++;
        }
        if (c > 0)
            d++;
        ans *= (c + 1);
        i++;
        p1 = v[i];
    }
    if (n != 1)
    {
        ans *= 2;
        ans -= 1;
    }
    cout << ans - d << endl;

    return 0;
}