John McCarthy wrote:
Edwin Clark wrote:
A friend of mine is seeking a name for a set (or multiset) of numbers that has the property
(*) every number in the set is no larger than the sum of the other numbers in the set.
Call such sets "weakly egalitarian" - like the US. Not even Bill Gates has most of of the money in the country - as yet.
Thinking of John McCarthy's suggestion, I just submitted the following sequence to the OEIS 1, 3, 6, 11, 18, 28, 42, 61, 86, 119, 162, 217, 287, 375 The nth term is the number of subsets S of {1,2,...,n} which contain a number that is greater than the sum of the other numbers in S. Actually this is just 2^n-1-b(n) where b(n) is the number of "weakly egalitarian" non-empty subsets of {1,...,n}. But somehow it seems simpler. Perhaps someone can find a nice formula for the nth term. --Edwin