A096859 Function A062401(x) = phi(sigma(x)) = f(x) is iterated. Starting with n, a(n) is the count of distinct terms arising in trajectory; a(n)=t(n)+c(n)=t+c, where t=number of transient terms, c=number of recurrent terms (in the terminal cycle).

1, 1, 2, 2, 2, 2, 3, 1, 2, 3, 3, 1, 3, 2, 2, 3, 3, 4, 2, 2, 4, 2, 2, 3, 4, 2, 4, 4, 2, 3, 4, 4, 4, 5, 4, 3, 5, 4, 4, 4, 2, 5, 3, 4, 4, 4, 4, 2, 4, 3, 4, 6, 5, 5, 4, 5, 5, 4, 4, 2, 4, 5, 3, 4, 4, 3, 5, 4, 5, 3, 4, 2, 4, 4, 3, 3, 5, 3, 5, 3, 4, 4, 4, 3, 4, 5, 5, 3, 4, 3, 3, 3, 5, 3, 5, 2, 6, 4, 3, 7, 5, 3, 3, 3, 5

Offset

1,3

Links

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

Example

n=255: list={255,144,360,288,[432,480],432,...}, t=transient=4, c=cycle=2, a(255)=t+c=6;
n=244: list={244,180,144,360,288,[432,480],432,...}, t=5, c=2, a(244)=7.

Mathematica

fs[x_] :=EulerPhi[DivisorSigma[1, x]] itef[x_, len_] :=NestList[fs, x, len] Table[Length[Union[itef[2^w, 20]]], {w, 1, 256}] (* len=20 at n<=256 is suitable *)

Prog

(Scheme) (define (A096859 n) (let loop ((visited (list n)) (i 1)) (let ((next (A062401 (car visited)))) (cond ((member next visited) i) (else (loop (cons next visited) (+ 1 i))))))) ;; Antti Karttunen, Nov 18 2017

Crossrefs

Cf. A000010, A000203, A062401, A062402, A095955, A096860, A096861, A096865.

Cf. also A096862.

Sequence in context: A280667 A194286 A063473 * A301304 A005086 A358333

Adjacent sequences: A096856 A096857 A096858 * A096860 A096861 A096862

Keyword

nonn

Author

Labos Elemer, Jul 21 2004

Status

approved