Attn. Eric

[Maximilian Hasler]

> http://mathworld.wolfram.com/PrimeSignature.html states
>    By definition, the prime signature of 1 is {1}.

This might be a convention not universally agreed upon,
e.g. on Wikipedia, 1 is not listed as a number having {1} as prime signature.

> By definition, the prime signature of n is the multiset of nonzero exponents
> in the prime factorization of n.  There are no nonzero exponents in the
> prime factorization of 1. Consequently the prime signature of 1 is the empty
> multiset {}.
> Maybe the prime signature of 1 is {1} by convention, but by definition it is {}.

I agree completely.
But one has to accept that in some specialized topics, there are
several inequivalent definitions available "on the market", which are
all reasonably defendable;
e.g. Rings may or may not have a unit, algebras may or may not be
associative,...
I also remember that the definition of "squareful" on MathWorld (which
is different from the definition of squarefull = 2-full on this same
web site) is not universally agreed upon (to several people, it may
mean the same than 2-full, in the spirit of Golomb's powerful
numbers).
There are other ongoing discussions about some conventions on MathWorld...

Concerning the prime signature related sequence I sent a copy of to seqfan,
I hesitated between defining it with offset 2, but then I decided in
favour of the idea of defining it (a bit vaguely as "a representation"
of the prime signature, on purpose using this term in view of the
"fuzzyness" it allows for)
in the way I defined it, namely as sum(10^(...) e[i]), in which case
the empty product (which is the prime factorization of 1) leads to an
empty sum which has the value 0 [as universally agreed upon].

On contrast, the sequence A037916 should (IMHO) strictly speaking have
offset 2 and not have the leading term 0, which seems here in
contradiction to the definition.

Maximilian
PS: also note that on Mathworld the multisets are written in
increasing order (like in my submitted sequence) while on Wikipedia
they are written in decreasing order. But this really does not make
much of a difference, and I think both conventions are commonly in
use.
PPS: I also noted that "floor" in the %C of my sequence should read
"ceil", but since Neil is overbooked, this can wait some time for
correction.