[seqfan] Re: Questions on A230492

[Vladimir Shevelev]

Not quite: from 2*p divisors only p possess such a property.

Vladimir
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Jack Brennen [jfb at brennen.net]
Sent: 20 December 2013 19:42
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: Questions on A230492

No need to check the even perfect numbers; yes, they are all in
A230492.  The proof is fairly easy to see because each even
perfect number satisfies the property that any divisor N is
at least equal to the sum of all of the smaller divisors.





On 12/19/2013 6:21 PM, Donovan Johnson wrote:
> Michel,
>
> The 7th perfect number is also a term in A230492. I checked all 2^38-1 positive sums. Each one is >= the previous sum. 524288 times they are equal.
>
> Donovan
>
>
>
>
>
> On Thursday, December 19, 2013 3:52 PM, Donovan Johnson <donovan.johnson at yahoo.com> wrote:
>
> Michel,
>
> The 6th perfect number is a term in A230492. I checked all 2^34-1 positive sums. Each one is >= the previous sum. 131072 times they are equal.
>
> I am checking the 7th perfect number right now.
>
> Regards,
> Donovan
>
>
>
>
>
>
> On Thursday, December 19, 2013 12:33 PM, "michel.marcus at free.fr" <michel.marcus at free.fr> wrote:
>
>
> Hi SeqFans,
>
> I have recently extended A230492 to 250 terms. Unless mistaken, it still verify the property that even terms are perfect.
> I have also checked that the 5 first perfect numbers (A000396) belong to this sequence (the 6th one is taking some time).
>
> Is it possible to prove that perfect numbers are in A230492, but no other even numbers ?
> And what could be said about the odd terms ?
>
> I have searched the OEIS and found only 2 other sequences with the same property:
> A034897   Hyperperfect numbers.
> A225417   Composite numbers which contain their sum of
>   aliquot parts as a substring.
> Are there others ?
>
> Thank you for your help.
> Michel
>
>
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