A096860 Function A062401(x) = phi(sigma(x)) = f(x) is iterated. Starting with n, a(n) is the count of distinct terms arising in the transient of this trajectory, that is: a(n) = A096859(n) - A095955(n).

0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 0, 2, 1, 1, 4, 2, 3, 1, 3, 3, 1, 1, 0, 1, 3, 1, 2, 1, 1, 3, 2, 3, 1, 1, 0, 2, 2, 1, 1, 3, 1, 3, 1, 2, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 3, 1, 3, 0, 4, 2, 1, 5, 3, 1, 1, 1, 3

Offset

1,32

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=4;
n=244: list={244,180,144,360,288,[432,480],432,...}, a(244)=4.
a(n)=0 means that n is a recurrent term from A096850.

Mathematica

With[{nn = 120}, Array[Length@ Union@ # - Length@ Select[Tally@ #, Last@ # > 1 &] &@ NestList[EulerPhi@ DivisorSigma[1, #] &, #, nn] &, 105]] (* Michael De Vlieger, Nov 18 2017 *)

Prog

(Scheme) (define (A096860 n) (let loop ((visited (list n))) (let ((next (A062401 (car visited)))) (cond ((member next visited) => (lambda (transientplusone) (- (length transientplusone) 1))) (else (loop (cons next visited))))))) ;; Antti Karttunen, Nov 18 2017

Crossrefs

Cf. A000010, A000203, A062401, A062402, A095955, A096859, A096861, A096865.

Cf. also A096863.

Sequence in context: A359537 A081653 A249615 * A128185 A175244 A206722

Adjacent sequences: A096857 A096858 A096859 * A096861 A096862 A096863

Keyword

nonn

Author

Labos Elemer, Jul 21 2004

Status

approved