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A225320 The number of iterations of the bi-unitary totient A116550 needed to reach 1 starting with n.

%I A225320 #17 Jul 16 2022 07:14:21
%S A225320 0,1,2,3,4,3,4,5,6,4,5,6,7,7,7,8,9,7,8,8,8,8,9,10,11,8,9,9,10,8,9,10,
%T A225320 10,11,12,11,12,10,10,10,11,9,10,13,12,11,12,12,13,12,13,10,11,11,10,
%U A225320 12,10,10,11,12,13,13,14,15,13,13,14,13,14,11,12,14,15,12,13,15,14,10,11,14
%N A225320 The number of iterations of the bi-unitary totient A116550 needed to reach 1 starting with n.
%H A225320 Amiram Eldar, <a href="/A225320/b225320.txt">Table of n, a(n) for n = 1..10000</a>
%F A225320 The smallest x such that A116550^x(n) = 1, where the operation Op^x denotes x nestings of the operator Op.
%e A225320 a(6) = 3 because the first step is A116550(6) = 3, the second A116550(3) = 2, the third A116550(2) = 1, where 1 is reached.
%p A225320 A225320 := proc(n)
%p A225320     option remember;
%p A225320     if n = 1 then
%p A225320         0;
%p A225320     else
%p A225320         1+procname(A116550(n)) ;
%p A225320     end if;
%p A225320 end proc:
%t A225320 A116550[1] = 1; A116550[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; a[n_] := a[n] = If[n == 1, 0, 1 + a[A116550[n]]]; Table[a[n], {n, 1, 80}] (* _Jean-François Alcover_, Dec 16 2013 *)
%Y A225320 Cf. A005424 (positions of records), A116550.
%K A225320 nonn
%O A225320 1,3
%A A225320 _R. J. Mathar_, May 05 2013