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%I A327407 #6 Sep 20 2019 08:57:22
%S A327407 0,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,2,1,3,1,1,1,1,1,1,1,
%T A327407 1,2,1,1,2,1,1,2,1,1,2,1,1,1,2,2,1,1,1,3,1,1,2,1,1,1,1,1,3,1,2,1,1,1,
%U A327407 1,1,1,2,1,1,2,1,1,2,1,1,4,1,1,2,1,1,2
%N A327407 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient over the maximum divisor that is 1, prime, or whose prime indices are pairwise coprime. (A327389, A327401).
%C A327407 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, prime, or whose prime indices are pairwise coprime are listed in A302569.
%H A327407 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%e A327407 We have 441 -> 63 -> 9 -> 3 -> 1, so a(441) = 4.
%t A327407 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327407 Table[Length[FixedPointList[#/Max[Select[Divisors[#],#==1||PrimeQ[#]||CoprimeQ@@primeMS[#]&]]&,n]]-2,{n,100}]
%Y A327407 See link for additional cross-references.
%Y A327407 Cf. A000005, A006530, A056239, A112798, A302569, A304711.
%K A327407 nonn
%O A327407 1,9
%A A327407 _Gus Wiseman_, Sep 20 2019

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