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A097035 Initial values for the iteration of the function f(x) = A063919(x) such that the iteration ends in a 5-cycle, i.e., in A097024.

%I A097035 #15 Jan 29 2024 13:49:08
%S A097035 570,870,1230,1290,1326,1482,1530,1686,1698,1710,1794,1866,1878,1890,
%T A097035 2058,2070,2142,2154,2166,2178,2238,2250,2502,2802,2814,3042,3222,
%U A097035 3630,3702,3714,3726,4350,4494,4506,4518,4914,5010,5142,5154,5166,5284,5418
%N A097035 Initial values for the iteration of the function f(x) = A063919(x) such that the iteration ends in a 5-cycle, i.e., in A097024.
%e A097035 n = 570: list = {570, 870, 1290, [1878, 1890, 2142, 2178, 1482], 1878}; after 3 transients, a 5-cycle arises.
%e A097035 n = 1230: {1230, 1794, 2238, 2250, 1530, 1710, [1890, 2142, 2178, 1482, 1878]} ; the iteration to the 5-cycle is not necessarily monotone. - _Hartmut F. W. Hoft_, Jan 25 2024
%t A097035 a063919[1] = 1; (* function a[] in A063919 by _Jean-François Alcover_ *)
%t A097035 a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/;n>1
%t A097035 a097035Q[k_] := Module[{iter=NestWhileList[a063919, k, UnsameQ, All]}, Apply[Subtract, Reverse[Flatten[Position[iter, Last[iter]], 1]]]==5]
%t A097035 a097035[n_] := Select[Range[n], a097035Q]
%t A097035 a097035[5418] (* _Hartmut F. W. Hoft_, Jan 25 2024 *)
%Y A097035 Cf. A002827, A063919, A063991, A097024, A097030-A097037.
%K A097035 nonn
%O A097035 1,1
%A A097035 _Labos Elemer_, Aug 30 2004