Consider the set of all strictly decreasing sequences of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
natural numbers having the property that in each sequence no term divides any other term of the sequence. Let
![A = (a_j)](/media/m/e/0/0/e0096ed075c9a0bdd39321b8f629a685.png)
and
![B = (b_j)](/media/m/2/5/4/2548e8065703b1c297b95bf18f11cffb.png)
be any two such sequences. We say that
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
precedes
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
if for some
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
,
![a_k < b_k](/media/m/a/5/9/a5965370a1194c4e66d2f8d229d07168.png)
and
![a_i = b_i](/media/m/a/1/4/a14c2c4bcf2e390c35936b94a25a4990.png)
for
![i < k](/media/m/e/b/2/eb2cdb5cd4efef1cd877e3774b7f865b.png)
. 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.