[seqfan] Destinies of sums of proper divisors.

Tanya Khovanova mathoflove-seqfan at yahoo.com
Sat Jul 4 17:32:49 CEST 2009

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.


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