

A097030


Numbers in the cycleattractors 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
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OFFSET

1,1


COMMENTS

This sequence collects 14cycleattractor elements for iteration of sumproperunitarydivisors.
A002827 provides 1cycle terms = unitary perfect numbers.
A063991 gives 2cycle elements = unitary amicable numbers.
A097024 collects true 5cycle elements, i.e., terms in endcycle of length 5 when A063919(x) function is iterated.
Concerning 3cycle elements, only {30,42,54} were encountered.


LINKS



EXAMPLE

These 42 numbers are in 3 different 14cycles. 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[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]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



