Colin Mallows's problems

[Max]

Ralf Stephan wrote:
> I submit:
> (what was your full name, Max?)

Max Alekseyev

> 
> %I A000001
> %S A000001 1,2,2,4,2,6,2,8,4,6,2,17,2,6,6,16,2,18,2,17
> %N A000001 Number of polynomials with coefficients in {0,1} that divide x^n-1.
> %K A000001 nonn,more
> %O A000001 1
> %A A000001 Ralf Stephan, following a suggestion from Max, Jun 11 2005
> 
> %I A000001
> %S A000001 1,2,2,4,2,6,2,8,4,6,2,17,2,6,6,16,2,18,2,17
> %N A000001 Number of polynomials p with coefficients in {0,1} that divide x^n-1 and such that (x^n-1)/{p(x-1)} has all coefficients in {0,1}.
> %K A000001 nonn,more
> %O A000001 1
> %A A000001 Ralf Stephan, following a suggestion from Max, Jun 11 2005
> 
> Are they the same?

Wow! I would be really surprised if they are the same.
The height norm implies that all coefficients of (x^n-1)/{p*(x-1)} are 1,0,-1.
But I do not see any reason why we would never have -1 as a coefficient of (x^n-1)/{p*(x-1)}.

Thanks,
Max