The Mompox Sequence, $a(n):=1, 2, 6, 24, 120, 20, \ldots$ (OEIS A008336), is the sequence of positive integers whose first term is $1$, and in which the $n$-th term (after the first one) equals the previous term divided by $n$ if the result is an integer, or times $n$ if not.

Is the Mompox sequence an S-sequence (S-sequences are described here), that is, are all its terms distinct?