A097030 Numbers in the cycle-attractors of length=14 of the function f(x)=A063919(x).

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

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