Let us define a sequence S(N):
= sum of all factors of an-1
itself. Most sequences either converge or begin to repeat.
S(12) → 12,16,15,9,4,3,1,1,1...
S(6) → 6,6,6,6,...
S(220) → 220,284,220,284,220,284,...
Try to evaluate S(50), S(80), S(99).
How about S(138)?
WILL IT CONVERGE TO 1,1,1,...?
(In reply to computer solution
Each of these is the Aliquot sequence of a number. Many of the interesting things you noticed are here:
6 and 28 are perfect numbers. You table ends before the next which is 496.
220 and 284 are the first pair of amicable numbers.
276 is the first of a few numbers with unknown end behavior, but it is conjectured they do become periodic at some point.
Posted by Jer
on 2018-05-10 14:46:46