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%I #13 Dec 02 2021 15:40:35
%S 0,0,0,0,1,0,2,0,0,1,1,0,3,2,1,0,1,0,1,1,2,1,2,0,1,3,0,2,2,1,1,0,1,1,
%T 2,0,4,1,3,1,3,2,2,1,1,2,1,0,2,1,1,3,2,0,1,2,1,2,1,1,2,1,2,0,3,1,2,1,
%U 2,2,3,0,2,4,1,1,2,3,3,1,0,3,1,2,1,2,2,1,2,1,3,2,1,1,1,0,4,2,1,1,1,1,3,3,2
%N Number of iterations in A064553 to reach a fixed point.
%C This is well-defined since A064553(n) <= n.
%H Antti Karttunen, <a href="/A064559/b064559.txt">Table of n, a(n) for n = 1..10000</a>
%F a(A003586(n)) = 0.
%e a(12) = 0 as A064553(12) = 12.
%e a(26) = 3 as A064553(26) = 14, A064553(14) = 10, A064553(10) = 8 and A064553(8) = 8.
%t b[n_] := b[n] = If[n == 1, 1, Times @@ (PrimePi[#[[1]]]^#[[2]]& /@ FactorInteger[n])];
%t c[n_] := c[n] = If[n == 1, 1, If[PrimeQ[n], Prime[PrimePi[n] + 1], Times @@ (c[#1]^#2& @@@ FactorInteger[n])]];
%t A064553[n_] := b[c[n]];
%t a[n_] := Length[FixedPointList[A064553, n]] - 2;
%t Array[a, 105] (* _Jean-François Alcover_, Dec 02 2021 *)
%o (Scheme) (define (A064559 n) (let ((k (A064553 n))) (if (= k n) 0 (+ 1 (A064559 k))))) ;; _Antti Karttunen_, Jul 23 2017
%Y Cf. A064553.
%K nonn
%O 1,7
%A _Reinhard Zumkeller_, Sep 21 2001
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