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.

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

Offset: 1

Author

Labos Elemer, Jul 21 2004

Keywords

• nonn
• look

Examples

			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.
		

Links

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

Crossrefs

Cf. A062401, A062402, A066437, A096862, A096863, A096866 (smallest term), A096993.

Cf. also A096861.

Programs

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 *)

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

Formula

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