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A037159 Consider the trajectory of n under the iteration of a map which sends x to 3x - sigma(x) if this is >= 0; otherwise the iteration stops. The sequence gives values of n which eventually reach 0.

%I A037159 #17 Jul 30 2020 15:09:39
%S A037159 82,120,280,672,1464,3048,4964,5568,5688,7666,8969,9176,9288,9514,
%T A037159 9616,9706,10132,10186,10232,10478,11496,11884,11914,12232,12320,
%U A037159 12820,13248,13842,13854,13866,14848,15076,15098,15196,15364,15586,15892
%N A037159 Consider the trajectory of n under the iteration of a map which sends x to 3x - sigma(x) if this is >= 0; otherwise the iteration stops. The sequence gives values of n which eventually reach 0.
%C A037159 A perfect number is a fixed point of this map.
%e A037159 82 -> 120 -> 0.
%t A037159 max = 16000; f[0] = 0; f[n_ /; 0 < n < 9max] := 3n - DivisorSigma[1, n]; f[_] = -1; Select[ Range[max], FixedPoint[f, #] == 0 &] (* _Jean-François Alcover_, Feb 22 2012 *)
%Y A037159 To see why 1, 16 and 23 are not in the sequence, see A058541, A058542 and A058545.
%Y A037159 Cf. A033885, A033945, A033946, A037160.
%K A037159 nonn,nice
%O A037159 1,1
%A A037159 _Naohiro Nomoto_
%E A037159 Better description from _Jud McCranie_, Dec 24 2000
%E A037159 Definition clarified by _Harvey P. Dale_, Jul 30 2020