Start with a set of a few distinct natural numbers.
For any 2 members, add their least common multiple to the set, if and only if it was not already in the set.
Continue the task until it cannot be done.
Call the result a final list.
Examples:
a. (2,4,8,16) a is a final list.
b. (2,3,4,6) will become a final list once we add number 12 to the set.
What can be the longest final list, if the initial set had 10 distinct numbers?
2^10 - 1.
For instance, if the initial set had 10 primes, then the full set is the set of all products of the numbers in any non-empty subset of the 10 primes.
In general, n primes lead to a full set of 2^n - 1.
For instance, {2,3,5} generates a final set of {2,3,5,6,10,15,30}
/*********************************************/
Edited to reflect Ady's preferred wording
Edited on January 28, 2018, 6:58 pm
D1 (spoiler)
