%I #6 Sep 20 2019 08:57:22

%S 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 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 1,1,1,2,1,1,2,1,1,2,1,1,4,1,1,2,1,1,2

%N 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 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 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 We have 441 -> 63 -> 9 -> 3 -> 1, so a(441) = 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||PrimeQ[#]||CoprimeQ@@primeMS[#]&]]&,n]]-2,{n,100}]

%Y See link for additional cross-references.

%Y Cf. A000005, A006530, A056239, A112798, A302569, A304711.

%K nonn

%O 1,9

%A _Gus Wiseman_, Sep 20 2019