A096860 - OEIS

%I #16 Nov 18 2017 20:59:52

%S 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,

%T 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,

%U 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

%N 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).

%H Antti Karttunen, <a href="/A096860/b096860.txt">Table of n, a(n) for n = 1..16384</a>

%e n=255: list={255,144,360,288,[432,480],432,...}, t=transient=4, c=cycle=2, a(255)=t=4;

%e n=244: list={244,180,144,360,288,[432,480],432,...}, a(244)=4.

%e a(n)=0 means that n is a recurrent term from A096850.

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

%o (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

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

%Y Cf. also A096863.

%K nonn

%O 1,32

%A _Labos Elemer_, Jul 21 2004