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%I #5 Sep 20 2019 08:57:55
%S 0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,
%T 1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U 1,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,0
%N Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1, 2, or a nonprime number whose prime indices are pairwise coprime (A327512, A327514).
%C Positions of zeros are A289509.
%C First term > 1 is a(225) = 2.
%C First zero not in A318978 is a(17719) = 0.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers that are 1, 2, or a nonprime number whose prime indices are pairwise coprime are listed in A302696.
%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%F a(15^n) = n.
%e We have 50625 -> 3375 -> 225 -> 15 -> 1, so a(50625) = 4.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Length[FixedPointList[#/Max[Select[Divisors[#],#==1||CoprimeQ@@primeMS[#]&]]&,n]]-2,{n,100}]
%Y See link for additional cross-references.
%Y Cf. A000005, A006530, A056239, A112798, A289509, A302569, A302696, A304711.
%K nonn
%O 1
%A _Gus Wiseman_, Sep 19 2019
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