A096865 Function A062401(x) = phi(sigma(x)) is iterated. Starting with n, a(n) is the smallest term arising in trajectory, either in transient or in terminal cycle.

1, 2, 2, 4, 2, 4, 4, 8, 9, 4, 4, 12, 4, 8, 8, 16, 4, 16, 8, 12, 16, 12, 8, 16, 16, 12, 16, 16, 8, 16, 16, 32, 16, 16, 16, 36, 16, 16, 16, 16, 12, 32, 12, 16, 16, 16, 16, 48, 36, 48, 16, 32, 16, 32, 16, 32, 32, 16, 16, 48, 16, 32, 48, 64, 16, 48, 32, 36, 32, 48, 16, 72, 36, 36, 48

Offset

1,2

Links

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

Example

n=255: list={255,144,360,288,[432,480],432,...}, a(255)=144 as a transient term;
n=254: list={254,[128],128,...}, a(254)=128, as a fixed point.

Mathematica

fs[x_] :=EulerPhi[DivisorSigma[1, x]] itef[x_, hos_] :=NestList[fs, x, hos] Table[Min[itef[w, 20]], {w, 1, 256}]

Prog

(Scheme) (define (A096865 n) (let loop ((visited (list n)) (m n)) (let ((next (A062401 (car visited)))) (cond ((member next visited) m) (else (loop (cons next visited) (min m next))))))) ;; Antti Karttunen, Nov 18 2017

Crossrefs

Cf. A062401, A062402, A095955, A096859, A096860, A096861 (largest term).

Cf. also A096866.

Sequence in context: A285741 A364567 A161831 * A116466 A116467 A079314

Adjacent sequences: A096862 A096863 A096864 * A096866 A096867 A096868

Keyword

nonn

Author

Labos Elemer, Jul 21 2004

Status

approved