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%I A327659 #4 Sep 22 2019 08:06:16
%S A327659 1,1,1,1,2,1,1,1,1,2,1,2,3,1,1,1,2,1,1,1,2,1,2,1,1,4,2,1,1,1,1,5,1,2,
%T A327659 1,2,1,1,1,1,1,2,1,2,4,2,3,1,2,1,2,1,1,4,1,1,1,2,1,1,2,4,1,1,1,2,2,7,
%U A327659 1,1,1,1,2,1,2,1,1,1,1,2,2,1,1,7,2,1,1
%N A327659 Number of factorizations of A318978(n - 1), the n-th number that is 1 or whose prime indices have a common divisor > 1, into numbers > 1 satisfying the same conditions.
%C A327659 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 whose prime indices have a common divisor > 1 are listed in A318978.
%H A327659 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 A327659 a(n) = A001055(A318978(n - 1)).
%t A327659 nn=100;
%t A327659 facsusing[s_,n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facsusing[Select[s,Divisible[n/d,#]&],n/d],Min@@#>=d&]],{d,Select[s,Divisible[n,#]&]}]];
%t A327659 y=Select[Range[1000],GCD@@PrimePi/@First/@FactorInteger[#]!=1&];
%t A327659 Table[Length[facsusing[Rest[y],n]],{n,y}]
%Y A327659 See link for additional cross-references.
%Y A327659 Cf. A056239, A112798, A281116, A289509, A318721, A327406.
%K A327659 nonn
%O A327659 1,5
%A A327659 _Gus Wiseman_, Sep 21 2019

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