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