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

David Wilson davidwwilson at comcast.net
Sun Jun 10 20:05:24 CEST 2012

Having authored A025487, I would beg to differ.

The prime signature of n is the multiset of positive exponents occurring 
in the prime factorization of n.

The prime signature of 1 is the empty multiset, since 1 has no prime 

Given the representation of multisets in A118914, it is correct that 
there are no terms associated with 1.

IMHO, 0 is not an acceptable substitute for the prime signature of 1. By 
the definition above, a prime signature is a multiset of positive 
integers, hence 0 cannot be an element of a prime signature.

Of course, when you submit a sequence, you can include whatever kludge 
you wish to represent 1, it is my observation that it is better to omit 
elements entirely than kludge them. Better to start at index 2 than to 
treat 1 inconsistently.

On 6/10/2012 7:14 AM, Matthew Vandermast wrote:
> Thanks, Charles.  Just to clarify the relevant part of a long email, I'm suggesting that a "signature" is distinguishable from a "multiset," and that 0 be used as the signature of the empty multiset in those sequences. I hope my suggestion will be acceptable, and it seems consistent with OEIS conventions to me.

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