# [seqfan] Re: Partitions of n

Neil Sloane njasloane at gmail.com
Sat Feb 1 19:09:50 CET 2014

```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
>
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>
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>

--
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
```