# [seqfan] Re: Destinies of sums of proper divisors.

Richard Guy rkg at cpsc.ucalgary.ca
Sat Jul 4 19:54:36 CEST 2009

```I suggest  0  as the destiny of  1
and  1  as the destiny of  2, 3, 4, 5,
7, 8, 9, ..., but it's a pretty boring
sequence.  I'd especially like to know
a(99225).  R.

On Sat, 4 Jul 2009, Tanya Khovanova wrote:

> Hello SeqFans,
>
> I propose a new sequence: a(n) is the smallest number in the destiny of n under the operation of "sum of proper divisors".
>
> Two numbers have the same destiny if they have the same tail in the aliquot sequence.
>
> For example, if we apply the sum of proper divisors to 95, we get a sequence:
> 95, 25, 6, 6, 6, 6, ... The destiny will be the cycle 6, 6, 6, 6, 6, ... Hence, a(95) = 6. Similarly, a(284) = a(220) = 220.
>
> I am not sure what this sequence should be for most numbers: 1 or 0?
>
> Note. This sequence might be undefined for 276.
>
> Tanya
>
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```