"1's proper divisors:  {}
2's proper divisors:  {1}
3's proper divisors:  {1}
4's proper divisors:  {1, 2}
5's proper divisors:  {1}
6's proper divisors:  {1, 2, 3}
7's proper divisors:  {1}
8's proper divisors:  {1, 2, 4}
9's proper divisors:  {1, 3}
10's proper divisors:  {1, 2, 5}

Largest number of proper divisors for any number from 1 to 20,000:  79
Numbers with this many:  15120, 18480"