[seqfan] Re: A083207 On an observation of Frank Buss.

[Christopher Gribble]

Yes Don.

Chris Gribble

-----Original Message-----
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Donald Alan Morrison
Sent: 01 August 2010 8:30 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A083207 On an observation of Frank Buss.

On Thu, Jul 8, 2010 at 11:58 AM, peter.luschny
<peter.luschny at googlemail.com> wrote:
> Recently numbers n whose divisors can be partitioned into two disjoint 
> sets whose sums are both sigma(n)/2, which were introduced by Reinhard 
> Zumkeller in 2003, got attention in the mathematical literature, in a 
> discussion on the Usenet de.sci.mathematik and by T. D. Noe on OEIS.
>
> Frank Buss examined the difference of consecutive Zumkeller numbers up 
> to 27188 and observed that greatest distance in this region is 12. (A 
> plot can be seen here [1]).

If you take the intersection of the zk numbers and the squarefree numbers
(in the same region), the intersection's max deltas will all be multiples of
12.  Their intersection contains no primes (since no zk can be prime).  The
zk numbers are a special case of the NP-Complete problem (the partition
problem).

Does anyone else find their intersection with the squarefree numbers
interesting?

Cheers,
Don


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