Imagine the following scenario: Once upon a time there was a tavern with 1000 beer taps, numbered from 1 to 1000. You were told by a mysterious stranger that the best beers are the one with the taps
- The sum of divisors (including 1, but not the number itself) of the tap number is greater than tap number itself
- No subset of those divisors sums up to the tap number itself The waiter is coming, what is your order? For example:
- Number 12: the proper divisors are 1, 2, 3, 4 and 6. The sum is 1+2+3+4+6 = 16 which is greater than 12 and matches the first condition. However, the subset 2+4+6=12 which violates the second condition.