The minimum of the antichains in the factor poset (Q1101454)

\(g(m,n)\) being the minimum of \(\min A,\) where A is a subset of \{1,2,...,m\} of size n and there do not exist two distinct x and y in A such that x divides y. A method of poset is used to prove that \(g(m,n)=2^ i\) for positive integer \(i\leq \log_ 3m\) and \(1+s(m,i- 1)<n\leq 1+s(m,i),\) where \(s(m,i)\) is the number of odd integers x such that \(m/3^ i<x\leq m.\)