Two. Because if there are three elements, their sum is bigger than any of the three - and the selected set has a maximum. I think there's a mistake, and this is not the intended question.

33, 34, 35, etc. evidently works, but I can't proof that it's not more.

jmerry wrote: Two. Because if there are three elements, their sum is bigger than any of the three - and the selected set has a maximum. I think there's a mistake, and this is not the intended question. I think there is like this, we colour the numbers, and sum of any 3 coloured numbers must not be other coloured number. and we want to know maximum number of coloured numbers

See here for generalized.