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

[Donald Alan Morrison]

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