[seqfan] Re: Partitions of n

Neil Sloane njasloane at gmail.com
Mon Feb 3 04:55:50 CET 2014


Jonathan, That's excellent - 2 new interesting sequences.
When you've submitted them, let me know the A-numbers,
please.
Best regards
Neil


On Sat, Feb 1, 2014 at 2:29 PM, jnthn stdhr <jstdhr at gmail.com> wrote:

> Actually, this sequence does include repetitions.  If I had used a(9) as an
> example that would have been clear.  The sequence without repetitions
> begins:  1, 1, 2 ,1, 1, 1, 11, 11, 7, 1, 15, 1, 7,...  This is also not in
> the database, so I will submit both.
>
> Thanks, Neil.
>
> Jonathan
>  On Feb 1, 2014 10:10 AM, "Neil Sloane" <njasloane at gmail.com> wrote:
>
> > Dear JS, Certainly it is worth adding to the OEIS!
> >
> > A perhaps clearer definition might be:
> >
> > Number of partitions of n such that the parts include all primes dividing
> > n.
> >
> > with a COMMENT saying
> >
> > If n is divisible by a power of a prime, we only need see one copy of
> that
> > prime.
> >
> > You might also add the companion sequence where you want to see all
> primes
> > dividing n (with repetition).
> >
> > Neil
> >
> >
> >
> >
> > On Sat, Feb 1, 2014 at 12:26 PM, jnthn stdhr <jstdhr at gmail.com> wrote:
> >
> > > Hello, seqers.
> > >
> > > If a(n) = the number of partitions of n having all factors of n, then
> > with
> > > n = (1,...,inf) we get the sequence:  0,1,1,1,1,1,1,2,3,3,1,7,1,15,...
> > >
> > > This sequence is easily  computed as follows:  Let p(n) be a partition
> > > counting function.  Then a(n) = p( n - sum( factors of n) ).  Example:
> > > a(10) = 3, because 10 = 2 * 5 -> 10 - (5 + 2) = 3 -> p(3) = 3 =
> > > {(3),(2,1),(1,1,1)}, and (5,2,3), (5,2,2,1), and (5,2,1,1,1) are the
> only
> > > partitions of 10 that have both 5 and 2 in them.
> > >
> > > This sequence isn't in the database.  Is it worth adding?
> > >
> > > Jonathan
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> >
> >
> > --
> > Dear Friends, I have now retired from AT&T. New coordinates:
> >
> > Neil J. A. Sloane, President, OEIS Foundation
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


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