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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.

%I A096864 #19 May 13 2019 14:01:25
%S A096864 1,2,3,4,12,6,12,12,12,12,18,12,28,14,15,16,72,18,72,20,28,22,36,24,
%T A096864 42,28,72,28,72,30,72,72,42,72,72,36,252,72,72,72,90,42,252,44,72,46,
%U A096864 72,72,252,50,252,72,252,72,90,72,252,72,90,72,168,72,252,252,168,66,168,252
%N 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.
%H A096864 Antti Karttunen, <a href="/A096864/b096864.txt">Table of n, a(n) for n = 1..16384</a>
%F A096864 a(n) = max(n, A066437(n)). - _Antti Karttunen_, Dec 06 2017
%e A096864 n=256: list={256,255,255}, a(256)=256 as a transient term;
%e A096864 n=101: list={101,217,546,403,1170,819,[1240,1512],1240,...}, a(101)=1512 as a cycle term.
%t A096864 gf[x_] :=DivisorSigma[1, EulerPhi[x]] gite[x_, hos_] :=NestList[gf, x, hos] Table[Max[gite[w, 20]], {w, 1, 256}]
%t A096864 Table[Max[NestList[DivisorSigma[1,EulerPhi[#]]&,n,20]],{n,70}] (* _Harvey P. Dale_, May 13 2019 *)
%o A096864 (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
%Y A096864 Cf. A062401, A062402, A066437, A096862, A096863, A096866 (smallest term), A096993.
%Y A096864 Cf. also A096861.
%K A096864 nonn,look
%O A096864 1,2
%A A096864 _Labos Elemer_, Jul 21 2004