Consider the set of all strictly decreasing sequences of
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natural numbers having the property that in each sequence no term divides any other term of the sequence. Let
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and
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be any two such sequences. We say that
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precedes
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if for some
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,
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and
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for
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. Find the terms of the first sequence of the set under this ordering.
%V0
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.