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Initial values for iteration of the function f(x) = A063919(x) such that the iteration ends in a 14-cycle, i.e., in A097030.
5

%I #14 Jan 29 2024 13:48:50

%S 1506,1518,1806,1902,1914,1938,1950,2226,2382,2394,2406,2418,2478,

%T 2826,2910,2946,2958,3234,3282,3294,3330,3510,3522,3534,3546,3582,

%U 3642,3654,3774,3906,3954,3966,3978,4146,4158,4194,4434,4446,4854,4866,4878,5262

%N Initial values for iteration of the function f(x) = A063919(x) such that the iteration ends in a 14-cycle, i.e., in A097030.

%e n=1506 is here because its iteration list = {1506, 1518, 1938, 2382, 2394, 2406, [2418, ...., 3582, 2418}. After a transient of length 6, the iteration ends in a cycle of length 14.

%t a063919[1] = 1; (* function a[] in A063919 by Jean-François Alcover *)

%t a063919[n_] :=

%t Total[Select[Divisors[n], GCD[#, n/#] == 1 &]] - n /; n > 1

%t a097034Q[k_] :=

%t Module[{iter = NestWhileList[a063919, k, UnsameQ, All]},

%t Apply[Subtract, Reverse[Flatten[Position[iter, Last[iter]], 1]]] ==

%t 14]

%t a097034[n_] := Select[Range[n], a097034Q]

%t a097034[5262] (* _Hartmut F. W. Hoft_, Jan 25 2024 *)

%Y Cf. A002827, A063919, A063991, A097024, A097030-A097037.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 30 2004