Number of divisors of num and denom of harmonic #s

[Leroy Quet]

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.

Franklin T. Adams-Watters

-----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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