[seqfan] Re: Partitions of n

jnthn stdhr jstdhr at gmail.com
Sat Feb 1 20:29:18 CET 2014


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
>
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>
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>


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