A097034 - OEIS

A097034

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

1506, 1518, 1806, 1902, 1914, 1938, 1950, 2226, 2382, 2394, 2406, 2418, 2478, 2826, 2910, 2946, 2958, 3234, 3282, 3294, 3330, 3510, 3522, 3534, 3546, 3582, 3642, 3654, 3774, 3906, 3954, 3966, 3978, 4146, 4158, 4194, 4434, 4446, 4854, 4866, 4878, 5262

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

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.

MATHEMATICA

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

a063919[n_] :=

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

a097034Q[k_] :=

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

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

14]

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

a097034[5262] (* Hartmut F. W. Hoft, Jan 25 2024 *)

CROSSREFS

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