[seqfan] Re: Orderly Numbers

T. D. Noe noe at sspectra.com
Fri Oct 30 17:12:30 CET 2009

At 9:05 AM -0700 10/30/09, Andrew Weimholt wrote:
>On Fri, Oct 30, 2009 at 8:34 AM, Alonso Del Arte
><alonso.delarte at gmail.com> wrote:
>> A potentially dumb question, but: how do you choose the k for each n? Are
>> there "orderly" numbers with only one choice for k and others with lots of
>> choices?
>> Al
>Yes, some orderly numbers have only 1 choice of k, and some have more.
>For example, for n=8, k can only be 5, but for n=71, k can be 3, 23, or 69.
>Or search for k is limited to  tau(n) < k < n-1.

For composite orderly numbers n, it appears that k can be taken to be
tau(n)+1, tau(n)+3, or tau(n)+4.  Not sure why.


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