# Number of divisors of num and denom of harmonic #s

Leroy Quet qq-quet at mindspring.com
Tue May 29 18:29:02 CEST 2007

```Yes, that's correct.  A115623 is wrong.

Incidently, there is a simple relationship between these two sequences
(once corrected).  Each ordering, for a given partition sum, is the
conjugates of the other, taken in reverse order.  And the number of
distinct parts in a partition is not changed by taking the conjugate
(since it is the number of "corners" in the Ferrers diagram).  So each
sequence just reverses each row from the other.

Also, I think both sequences should have an initial 0 added, with the
offset changed to 0.  (Both actually have comments to this effect in
their names, of all things.  We should just make the changes and remove
the excess verbiage.)

I'm sending Neil edited sequences fixing both of these.

-----Original Message-----
From: Joshua Zucker <joshua.zucker at gmail.com>

On 5/23/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:

> A103921 and A115623 (Look very much alike, is the ordering ever
different?)

> http://www.research.att.com/~njas/sequences/?q=id:A103921|id:A115623

Aren't the partitions of 6 in Mathematica order

6,
5, 1,
4, 2,
4, 1, 1

which leads to a 1, 2, 2, 2 in the sequence A115623 (I see a 1,2,2,1
there)

while the partitions of 6 in Abramowitz-Stegun order are

6,
1, 5,
2, 4,
3, 3

which leads to a 1,2,2,1 in the sequence A103921?

In other words, I think maybe there's a mistake in A115623 that leads
to the apparent duplication.  Franklin?  You're the expert on these,
if I remember correctly from some seqfan exchanges some time ago.

--Joshua

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