Consider the set of all strictly decreasing sequences of
natural numbers having the property that in each sequence no term divides any other term of the sequence. Let
and
be any two such sequences. We say that
precedes
if for some
,
and
for
. Find the terms of the first sequence of the set under this ordering.
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Consider the set of all strictly decreasing sequences of $n$ natural numbers having the property that in each sequence no term divides any other term of the sequence. Let $A = (a_j)$ and $B = (b_j)$ be any two such sequences. We say that $A$ precedes $B$ if for some $k$, $a_k < b_k$ and $a_i = b_i$ for $i < k$. Find the terms of the first sequence of the set under this ordering.