/*
12: 2 3 4 6 
13:
14: 2 7

want a function factors(N) which e.g.
factors(12) prints 12: 2 3 4 6



void printall(int from, int to)
{ if (from <= to)
  { cout << from << " ";
    printall(from + 1, to); } }

printall(2, 11) would print 2 3 4 5 6 7 8 9 10 11

void printalldivisors(int N, int from, int to)
{ if (from <= to)
  { if (N % from == 0)
      cout << from << " ";
    printalldivisors(N, from + 1, to); } }

printalldivisors(12, 2, 11) would print 2 3 4 6 

void printalldivisors(int N, int from)
{ if (from <= N - 1)
  { if (N % from == 0)
      cout << from << " ";
    printalldivisors(N, from + 1); } }

printalldivisors(12, 2) would print 2 3 4 6 

now want a function that prints the same things, but
it also tells us how many divisors there were.
*/

#include <iostream>

using namespace std;

int count_and_print_all_divisors(int N, int from)
{ if (from <= N - 1)
  { if (N % from == 0)
    { cout << from << " ";
      int count = count_and_print_all_divisors(N, from + 1);
      return count + 1; }
    else
    { int count = count_and_print_all_divisors(N, from + 1);
      return count; } }
  return 0; }

void list_divisors(int from, int to)
{ if (from <= to)
  { cout << from << ": ";
    int N = count_and_print_all_divisors(from, 2);
    if (N == 0)
      cout << "(prime)";
    cout << "\n";
    list_divisors(from + 1, to); } }

// int main()
// { int N = count_and_print_all_divisors(240, 2);
//  cout << "\nthe number of divisors was " << N << "\n"; }

int main()
{ list_divisors(1, 24); }

/*
int count_and_print_all_divisors(int N, int from)
{ int total = 0;
  for (int i = from; i < N; i += 1)
  { if (N % i == 0)
    { cout << i << " ";
      count += 1; } }
  return count; }
*/