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 A097030 Numbers in the cycle-attractors of length=14 of the function f(x)=A063919(x). 22
 2418, 2958, 3522, 3534, 3582, 3774, 3906, 3954, 3966, 3978, 4146, 4158, 4434, 4446, 24180, 29580, 35220, 35238, 35340, 35820, 37740, 38682, 39060, 39540, 39660, 39780, 41460, 41580, 44340, 44460, 45402, 49878, 65190, 65322, 74430, 74610, 74790, 98106, 101478, 117258, 117270, 117450 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence collects 14-cycle-attractor elements for iteration of sum-proper-unitary-divisors. A002827 provides 1-cycle terms = unitary perfect numbers. A063991 gives 2-cycle elements = unitary amicable numbers. A097024 collects true 5-cycle elements, i.e., terms in end-cycle of length 5 when A063919(x) function is iterated. Concerning 3-cycle elements, only {30,42,54} were encountered. LINKS Table of n, a(n) for n=1..42. J. O. M. Pedersen, Known Unitary Sociable Numbers of order different from four [Via Internet Archive Wayback-Machine] J. O. M. Pedersen, Order 14 cycles, 2007. EXAMPLE 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] MATHEMATICA a063919[1] = 1; (* function a[] in A063919 by Jean-François Alcover *) a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/; n>1 a097030Q[k_] := Module[{a=NestList[a063919, k, 14]}, Count[a, k]==2&&Last[a]==k] a097030[n_] := Select[Range[n], a097030Q] a097030[117450] (* Hartmut F. W. Hoft, Jan 24 2024 *) CROSSREFS Cf. A063919, A002827, A063991, A097024. Sequence in context: A159346 A256835 A237940 * A204367 A131759 A254901 Adjacent sequences: A097027 A097028 A097029 * A097031 A097032 A097033 KEYWORD nonn AUTHOR Labos Elemer, Aug 30 2004 EXTENSIONS More terms from Michel Marcus, Sep 29 2018 STATUS approved

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Last modified June 13 10:24 EDT 2024. Contains 373383 sequences. (Running on oeis4.)