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

1,2

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: A099527 A354371 A345276 * A373576 A013620 A317498

Adjacent sequences: A096861 A096862 A096863 * A096865 A096866 A096867

Keyword

nonn,look

Author

Labos Elemer, Jul 21 2004

Status

approved