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

Richard Mathar mathar at strw.leidenuniv.nl
Sat Jul 4 18:28:28 CEST 2009

```tk> Date: Sat, 4 Jul 2009 08:32:49 -0700 (PDT)
tk> From: Tanya Khovanova <mathoflove-seqfan at yahoo.com>
tk> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
tk> Subject: [seqfan]  Destinies of sums of proper divisors.
tk> ...
tk> I propose a new sequence: a(n) is the smallest number in the destiny of n under the operation of "sum of proper divisors".
tk>
tk> Two numbers have the same destiny if they have the same tail in the aliquot sequence.
tk>
tk> For example, if we apply the sum of proper divisors to 95, we get a sequence:
tk> 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.
tk>
tk> I am not sure what this sequence should be for most numbers: 1 or 0?
tk>
tk> Note. This sequence might be undefined for 276.

Unfortunately that is like a re-writing of A126016, for which little is
known; any such new sequence would remain sparsely populated.

Richard

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