[seqfan] Re: Prime signature of 1, and second signature

[franktaw at netscape.net]

To me, it's clear that the best definition of the prime signature is 
that it is a multiset. But then, it is equally clear to me that 
partitions should be defined as multisets, although the traditional 
definition is otherwise.

Note, by the way, my definition of the signature of a partition in 
A115621. (Since I submitted this sequence, I have come to realize that 
this signature definition applies to any finite multiset, not just 
partitions.) If we regard the factorization of a number as a multiset 
of primes (another definition that seems obvious to me), the prime 
signature is then the signature of the prime factorization.

Franklin T. Adams-Watters