greedy computation of pseudoperfect numbers?

[T. D. Noe]

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
>
>
>