A number is an   attractive number   if the number of its prime factors (whether distinct or not) is also prime.



Example

The number   20,   whose prime decomposition is   2 × 2 × 5,   is an   attractive number   because the number of its prime factors   (3)   is also prime.



Task

Show sequence items up to   120.



Reference

   The OEIS entry:   A063989: Numbers with a prime number of prime divisors.


#include <iostream>
#include <iomanip>
 
#define MAX 120
 
using namespace std;
 
bool is_prime(int n) {   
    if (n < 2) return false;
    if (!(n % 2)) return n == 2;
    if (!(n % 3)) return n == 3;
    int d = 5;
    while (d *d <= n) {
        if (!(n % d)) return false;
        d += 2;
        if (!(n % d)) return false;
        d += 4;
    }
    return true;
}
 
int count_prime_factors(int n) {    
    if (n == 1) return 0;
    if (is_prime(n)) return 1;
    int count = 0, f = 2;
    while (true) {
        if (!(n % f)) {
            count++;
            n /= f;
            if (n == 1) return count;
            if (is_prime(n)) f = n;
        } 
        else if (f >= 3) f += 2;
        else f = 3;
    }
}
 
int main() {
    cout << "The attractive numbers up to and including " << MAX << " are:" << endl;
    for (int i = 1, count = 0; i <= MAX; ++i) {
        int n = count_prime_factors(i);
        if (is_prime(n)) {
            cout << setw(4) << i;
            if (!(++count % 20)) cout << endl;
        }
    }
    cout << endl;
    return 0;
}