S is a subset of the divisors of 2024^2024 such that no number in S has its own multiple in S.
What is the largest possible value of |S|?
(In reply to
A larger cardinality by Steve Herman)
Consider the set of ordered triplets of nonnegative integers with a sum of 2024. The number of such triplets is the 2025th triangular number 2025*2026/2 = 2051325.
Now generate a factor from triplet (a,b,c) by constructing factor 2^a * 11^b * 13^c. None of these factors can be a multiple of another, so they create a valid set S. Then |S| is at least 2051325.
However this is not the answer as there are clearly larger factors available like 2^4048.
I believe if the problem was about (2*11*13)^2024 then 2051325 would be the answer; but instead we have (2^3*11*13)^2024 to work with.
re: A larger cardinality - much much larger
