[seqfan] Re: Stumped on sums of perfect numbers

[Alonso Del Arte]

That's probably the best explanation. Then it might be acceptable to make a
small change to that sequence, not tag it dead, but Harvey's interpretation
should still become a new sequence.

Update on Torsten Klar: I've got a warning message telling me "delivery has
been delayed" but I "do not need to resend" the message.

Al

On Wed, Feb 8, 2012 at 7:39 PM, <franktaw at netscape.net> wrote:

> I think you get this result if you say "multiply perfect" instead of
> "perfect" (but excluding 1), and mistakenly include sigma(672) = 2016
> instead of 672 itself. (The reference is to A065997, which is n such that
> sigma(n)/n is prime; this may be what is intended. 30240 is the first
> difference from what I have suggested, and these values do not get that
> high.)
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Alonso Del Arte <alonso.delarte at gmail.com>
>
> Yesterday, Harvey noticed that A083865 doesn't quite fit with its
> definition, "perfect numbers and sums of perfect numbers." I am
> convinced that there is some thought process behind that sequence
> which wasn't written down and may now very well be forgotten. I have
> e-mailed Torsten, but while I wait for a response, I have pondered a
> number of different explanations, none of which are satisfactory for
> the numbers given.
>
> It is possible that perfect numbers may be used more than once. Thus,
> 120 = 3(28) + 6^2. But then why are numbers like 112 and 118 not in
> the sequence?
>
> Or maybe perfect numbers may be "repeated" if they have already been
> added in. Since 6 + 28 = 34, under this explanation we could then
> (after a(3)) do 6 + 28 + 34 = 68. But 68 is not in the sequence.
>
> Maybe k-perfect numbers are allowed. That would explain the presence
> of 120, as it is 3-perfect. But then why is 672 missing? And likewise
> 678, 700, 792, etc.
>
> I think that Harvey's interpretation of the current definition 6, 28,
> 34, 496, 502, 524, 530, 8128, ... merits to be a new sequence in its
> own right. And if we can't find a satisfactory explanation for
> A083865, maybe it should become a dead sequence.
>
> Al
>
> --
> Alonso del Arte
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> AlonsoDelarte <https://www.smashwords.com/profile/view/AlonsoDelarte>>
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> >
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-- 
Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
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