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

Charles Greathouse charles.greathouse at case.edu
Sun Jun 10 20:36:36 CEST 2012

I certainly agree as regards A025487.  It's less clear what to do with A212172.

Charles Greathouse
Case Western Reserve University

On Sun, Jun 10, 2012 at 2:05 PM, David Wilson <davidwwilson at comcast.net> wrote:
> 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
> divisors.
> 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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