possible error in A005835

[franktaw at netscape.net]

The comment is definitely wrong.

However, "proper divisors" is most often interpreted to mean only
that the number itself is excluded; 1 is not excluded.  (The
alternative interpretation is meant just often enough to be
confusing.)  Certainly in any context where one is talking about
perfect numbers this is the intended interpretation.

Franklin T. Adams-Watters

-----Original Message-----
From: Joerg Arndt <arndt at jjj.de>

Also it seems that 6 should _not_ be in the sequence:

pari/gp
N=72  \\ up to this value
vv=vector(N);
{ for(n=2, N,
     if ( isprime(n), next() );
     d=divisors(n);
     d=vector(#d-2,j,d[j+1]);  \\ not n, not 1
\\     print(n, ":: ", d);

     for (k=1, (1<<#d)-1,  \\ all subsets
        t=vecextract(d, k);
        if ( n==sum(j=1,#t,t[j]),
            vv[n] += 1;
\\            print(n, ": ", t);  \\ print subset that works
\\            break();  \\ speedup, just find one sum
        );
     );
  ); }

for (j=1, #vv, if (vv[j]>0, print1(j,", ")))  \\ A005835 (after 
correction)

\\ this prints:
12, 18, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72,



* Maximilian Hasler <maximilian.hasler at gmail.com> [Apr 06. 2008 13:16]:
> I agree, I sent the following message to Neil and to the author 7 days
> ago, so far without reply.
> Maximilian
> ---------- Forwarded message ----------
> From: Maximilian Hasler <Maximilian.Hasler at martinique.univ-ag.fr>
> Date: Sun, Mar 30, 2008 at 3:09 AM
> Subject: bug in A005835 ?
> To: "N. J. A. Sloane" <njas at research.att.com>,
> reinhard.zumkeller at gmail.com, reinhard.zumkeller at lhsystems.com
>
> I may misunderstand something, but IMO the %C is wrong, I'd rather be
>  tempted to say:
>
>  %C A005835 Weird numbers (A006037) are neither in this sequence,
>  neither in A005100.
>  - Maximilian F. Hasler (www.univ-ag.fr/~mhasler), Mar 30 2008
>
>
>  %I A005835 M4094
>  %S A005835 
6,12,18,20,24,28,30,36,40,42,48,54,56,60,66,72,78,80,84,88,90,96,100,102,

>  %N A005835 Pseudoperfect (or semiperfect) numbers: some set of proper
>  divisors of n sums to n.
>  %C A005835 A033630(a(n)) > 1; complement of A005100. - Reinhard
>  Zumkeller (reinhard.zumkeller(AT)gmail.com),
>                Mar 02 2007
>  (snip)