A100832: What exactly are amenable numbers?

[Alonso Del Arte]

The sequence of amenable numbers, A100832, was added today. I looked
to Mathworld for more information, there it says that all composites
are amenable. Wikipedia elaborates that

"One can always make an inelegant solution by taking the prime
factorization (expressed with repeated factors rather than exponents)
and add as many 1s as necessary to add up to n. Because of the
multiplicative identity, multiplying this set of integers will yield n
no matter how many 1s there are in the set."

Yet, some composites are not in the sequence, 4, 6, 10, 14, (in short,
all composites not congruent to 0 or 1 mod 4).

Wikipedia even goes on to say that any prime number can be amenable
with the set {1, -1, 1, -1, p}.

So what are the constraints on amenable numbers? Is the congruence
required? Are negative numbers allowed in the sets?

Alonso