greedy computation of pseudoperfect numbers?

[Maximilian Hasler]

smallest counter-example:
351351
Maximilian

On 4/8/08, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
> Can someone prove or find a counterexample
>  to the potential comment for A136446 --
>
>  ``odd members are A005231'' ??   R.
>
>
>  On Tue, 8 Apr 2008, T. D. Noe wrote:
>
>
> > At 8:45 AM -0400 4/8/08, Maximilian Hasler wrote:
> >
> > >
> > > > For both sorts of pseudoperfect numbers, allowing divisor one A005835,
> > > >  and forbidding divisor one A136446, a greedy method _seems_ to always
> > > >  work for deciding whther a given n in in the sequence:
> > > >
> > >
> >
> > Let d be the list of divisors of n (we can include or exclude 1).  Compute
> > terms of the polynomial product_i (1+x^d[i]) up to the x^n term.  (Perhaps
> > your PARI code does this. I don't read PARI.) If the x^n term is nonzero,
> > then n is the sum of a subset of the divisors in d.  This is fairly fast
> > and deterministic.  Using this method, the first 10 odd terms of A136446
> are
> >
> > 945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985
> >
> > which starts the same as A005231, odd abundant numbers.  Here is the
> > Mathematica code:
> >
> > t = {}; n = 1; While[Length[t] < 10, n = n + 2;
> > d = Rest[Most[Divisors[n]]];
> > c = SeriesCoefficient[
> >  Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n];
> > If[c > 0, AppendTo[t, n]]]; t
> >
> > Best regards,
> >
> > Tony
> >
> >
> >
> >
>