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A288636 Height of power-tower factorization of n. Row lengths of A278028.

%I A288636 #11 Nov 24 2017 10:09:11
%S A288636 0,1,1,2,1,1,1,2,2,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,2,1,1,
%T A288636 1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,
%U A288636 1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1
%N A288636 Height of power-tower factorization of n. Row lengths of A278028.
%C A288636 After a(1)=0 this sequence has many terms equal to A089723. It first differs at a(64)=2, A089723(64)=4.
%C A288636 First positions of a(n) = {0, 1, 2, 3, 4} are n = {1, 2, 4, 16, 65536}. - _Michael De Vlieger_, Nov 24 2017
%H A288636 Michael De Vlieger, <a href="/A288636/b288636.txt">Table of n, a(n) for n = 1..65536</a>
%t A288636 a[n_] := If[n == 1, 0, 1+a[GCD @@ FactorInteger[n][[All, 2]]]];
%t A288636 Array[a,100]
%Y A288636 Cf. A007916, A089723, A164337, A277562, A277564, A278028.
%K A288636 nonn
%O A288636 1,4
%A A288636 _Gus Wiseman_, Jun 12 2017