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A005424 Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.

%I A005424 M0530 #39 Jul 16 2022 07:09:38
%S A005424 2,3,4,5,8,9,13,16,17,24,25,35,44,63,64,91,97,128,193,221,259,324,353,
%T A005424 391,477,702,929,1188,1269,1589,1613,2017,2309,2623,3397,4064,4781,
%U A005424 5468,6515,6887,9213,12286,12887,14009,16564,16897,17803,30428,36256
%N A005424 Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.
%C A005424 Let p(n) = number of unitary divisors k of n, k<n, that are relatively prime to n. Let p_1(n) = p(n), p_r(n) = p(p_{r-1}(n)). Sequence gives minimal r such that p_r(n)=1.
%D A005424 M. Lal, H. Wareham and R. Mifflin, Iterates of the bi-unitary totient function, Utilitas Math., 10 (1976), 347-350.
%D A005424 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005424 Amiram Eldar, <a href="/A005424/b005424.txt">Table of n, a(n) for n = 1..97</a> (terms 1..78 from Donovan Johnson)
%p A005424 L := [seq(0,i=0..100)] ;
%p A005424 for n from 1 do
%p A005424     itr := A225320(n) ;
%p A005424     if itr < nops(L) then
%p A005424         if op(itr,L) = 0 then
%p A005424             L := subsop(itr=n,L) ;
%p A005424             print(L) ;
%p A005424         end if;
%p A005424     end if;
%p A005424 end do: # _R. J. Mathar_, May 02 2013
%t A005424 A116550[1] = 1; A116550[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; A225320[n_] := A225320[n] = If[n == 1, 0, 1+A225320[A116550[n]]]; L = Array[0&, 100]; For[n = 1, n <= 40000, n++, itr = A225320[n]; If[itr < Length[L], If[L[[itr]] == 0, L = ReplacePart[L, itr -> n]; Print[Select[L, Positive] // Last]]]]; Select[L, Positive] (* _Jean-François Alcover_, Jan 13 2014, after _R. J. Mathar_ *)
%Y A005424 Cf. A116550, A225175, A225176.
%K A005424 nonn,nice
%O A005424 1,1
%A A005424 _N. J. A. Sloane_