

A096864


Function A062402(x) = sigma(phi(x)) is iterated. Starting with n, a(n) is the largest term arising in trajectory, either in transient or in terminal cycle.


5



1, 2, 3, 4, 12, 6, 12, 12, 12, 12, 18, 12, 28, 14, 15, 16, 72, 18, 72, 20, 28, 22, 36, 24, 42, 28, 72, 28, 72, 30, 72, 72, 42, 72, 72, 36, 252, 72, 72, 72, 90, 42, 252, 44, 72, 46, 72, 72, 252, 50, 252, 72, 252, 72, 90, 72, 252, 72, 90, 72, 168, 72, 252, 252, 168, 66, 168, 252
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OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384


FORMULA

a(n) = max(n, A066437(n)).  Antti Karttunen, Dec 06 2017


EXAMPLE

n=256: list={256,255,255}, a(256)=256 as a transient term;
n=101: list={101,217,546,403,1170,819,[1240,1512],1240,...}, a(101)=1512 as a cycle term.


MATHEMATICA

gf[x_] :=DivisorSigma[1, EulerPhi[x]] gite[x_, hos_] :=NestList[gf, x, hos] Table[Max[gite[w, 20]], {w, 1, 256}]
Table[Max[NestList[DivisorSigma[1, EulerPhi[#]]&, n, 20]], {n, 70}] (* Harvey P. Dale, May 13 2019 *)


PROG

(Scheme) (define (A096864 n) (let loop ((visited (list n)) (m n)) (let ((next (A062402 (car visited)))) (cond ((member next visited) m) (else (loop (cons next visited) (max m next))))))) ;; Antti Karttunen, Nov 18 2017


CROSSREFS

Cf. A062401, A062402, A066437, A096862, A096863, A096866 (smallest term), A096993.
Cf. also A096861.
Sequence in context: A116054 A176621 A099527 * A013620 A317498 A119799
Adjacent sequences: A096861 A096862 A096863 * A096865 A096866 A096867


KEYWORD

nonn,look


AUTHOR

Labos Elemer, Jul 21 2004


STATUS

approved



