Colin Mallows's problems

[Max]

There are related sequences:

1) a(n) = the number of 01-polynomials (01-polynomial has all coefficients equal 0 or 1) dividing x^n-1.
There are at least two such polynomials for every n>1,
they are 1 and 1+x+...+x^(n-1)=(x^n-1)/(x-1).

2) The number of 01-polynomials p dividing x^n-1 such that (x^n-1)/(x-1)/p is a 01-polynomial as well.

Could anybody compute these and check if they are in OEIS?

Thanks,
Max


N. J. A. Sloane wrote:
> Mitch says:
> 
> 
>>> For each m,n, how many of these arrangments can be realised as the ordering 
>>>of numbers of the form x_i + y_j?
>>
>>Is there an example for this? I don't understand how this is supposed to 
>>work.
> 
> 
> 
> Me:  i assumed it was something like this:   certain of
> these arrangements can be obtained by taking m numbers x1 ... xm
> in increasing order of course
> and n numbers y1 ... yn, and filling the array with M_{i,j} = xi + yj.
> 
> If we are lucky, this will use all the numbers 1 ... mn exactly once
> - in how many ways can this be done?
> 
> NJAS
> 
>