GF for A067743

[Maximilian Hasler]

On Mon, May 12, 2008 at 3:32 PM, Joerg Arndt <arndt at jjj.de> wrote:
> I think the GF for A067743 is
> sum(k=1,N, z^(2*k^2)*(1+z^k)/(1-z^k) )

Seems correct.
My 2c of PARI (kept it simple, stupid...):

A067743(n)=sumdiv( n,d, d*d<n/2 || d*d >= 2*n )

A067742(n)=sumdiv( n,d, d*d >= n/2 && d*d < 2*n )

Maximilian
PS: just in case...
gp> vector(1001,n,n++;sumdiv(n,d, d*d<n/2|d*d>=2*n))==
Vec(sum(k=1,30, z^(2*k^2)*(1+z^k)/(1-z^k),O(z^1003) ))
time = 62 ms.
%280 = 1