|
%I #26 Jan 25 2024 08:02:16
%S 2418,2958,3522,3534,3582,3774,3906,3954,3966,3978,4146,4158,4434,
%T 4446,24180,29580,35220,35238,35340,35820,37740,38682,39060,39540,
%U 39660,39780,41460,41580,44340,44460,45402,49878,65190,65322,74430,74610,74790,98106,101478,117258,117270,117450
%N Numbers in the cycle-attractors of length=14 of the function f(x)=A063919(x).
%C This sequence collects 14-cycle-attractor elements for iteration of sum-proper-unitary-divisors.
%C A002827 provides 1-cycle terms = unitary perfect numbers.
%C A063991 gives 2-cycle elements = unitary amicable numbers.
%C A097024 collects true 5-cycle elements, i.e., terms in end-cycle of length 5 when A063919(x) function is iterated.
%C Concerning 3-cycle elements, only {30,42,54} were encountered.
%H J. O. M. Pedersen, <a href="http://web.archive.org/web/20130731050921/http://amicable.homepage.dk/knwnux.htm">Known Unitary Sociable Numbers of order different from four</a> [Via Internet Archive Wayback-Machine]
%H J. O. M. Pedersen, <a href="/A097030/a097030.txt">Order 14 cycles</a>, 2007.
%e These 42 numbers are in 3 different 14-cycles. The first is: [2418, 2958, 3522, 3534, 4146, 4158, 3906, 3774, 4434, 4446, 3954, 3966, 3978, 3582]. [edited by _Michel Marcus_, Sep 29 2018]
%t a063919[1] = 1; (* function a[] in A063919 by _Jean-François Alcover_ *)
%t a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/;n>1
%t a097030Q[k_] := Module[{a=NestList[a063919, k, 14]}, Count[a, k]==2&&Last[a]==k]
%t a097030[n_] := Select[Range[n], a097030Q]
%t a097030[117450] (* _Hartmut F. W. Hoft_, Jan 24 2024 *)
%Y Cf. A063919, A002827, A063991, A097024.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 30 2004
%E More terms from _Michel Marcus_, Sep 29 2018
|
