Thematics Of Order

[Antti Karttunen]

Peter Cameron wrote:

>On Fri, Apr 15, 2005 at 02:14:12PM -0400, Jon Awbrey wrote:
>  
>
>>How much of the additive, linear, or total order in the
>>sequence of natural numbers is "purely mutiplicative",
>>that is, how much of the order can be determined
>>solely by inspection of primes factorizations?
>>
>>    
>>
>I think it was Ulam who remarked that there are rings which are
>multiplicatively isomorphic to the integers but additively completely
>different. One striking example is the polynomial ring over the
>integers mod 3.
>
>Peter Cameron.
> 
>  
>

Inspired by this I propose a more practical question:
Can we find a nice "closed" (or somehow easily computed)
form for:
http://www.research.att.com/projects/OEIS?Anum=A061858

or a similar table involving the differences of ordinary
integer multiplication table and e.g. the mult. table of GF(3)[X].


Yours,

Antti Karttunen