# [seqfan] Re: A question concerning perfect numbers

Thu Oct 24 17:00:38 CEST 2013

```Thank you very much, Giovanni!
For example, for yours 2096128=2^10*23*89,
the sum of proper odious divisors is 23*89(1+2+...+2^9)+(1+2+...+2^10) =2047*1024=2096128.
But your calculations up to 10^9 show that these numbers
are much more rare than the numbers of a dual sequence A230587. In my opinion, it is interesting!

Best regards,

----- Original Message -----
From: Giovanni Resta <g.resta at iit.cnr.it>
Date: Thursday, October 24, 2013 1:23
Subject: [seqfan] Re: A question concerning perfect numbers
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> On 10/24/2013 12:13 PM, Vladimir Shevelev wrote:
>
> > My question is: are there non-perfect such numbers?
> > Note, that there are respectively "many" numbers n, for which
> all their proper evil divisors sum to n (we submit sequence A230587).
>
> Up to 10^9 the numbers I found are
>
> 28 = 2^2  * 7
> 496 = 2^4  * 31
> 8128 = 2^6  * 127
> 415800 = 2^3  * 3^3  * 5^2  * 7 * 11
> 2096128 = 2^10  * 23 * 89
> 33550336 = 2^12  * 8191
>
> so, 415800 and 2096128.
>
> Giovanni
>
>
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