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%I #5 Sep 16 2019 12:39:13
%S 1,1,1,1,2,1,2,1,1,2,2,1,1,2,2,1,2,1,5,1,2,2,2,1,2,2,1,5,1,2,1,2,1,2,
%T 2,2,1,1,2,2,5,1,2,5,1,1,2,2,5,1,2,1,2,2,2,1,2,2,2,2,1,1,5,1,5,2,1,1,
%U 5,2,1,5,2,2,2,2,2,1,2,5,1,2,2,1,5,1,2
%N Number of factorizations of the n-th squarefree number A005117(n) into squarefree numbers > 1.
%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(n) = A050320(A005117(n)) = A000110(A072047(n)) = A000110(A001222(A005117(n))).
%t nn=100;
%t 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 y=Select[Range[nn],SquareFreeQ];
%t Table[Length[facsusing[Rest[y],n]],{n,y}]
%Y See link for additional cross-references.
%Y Cf. A000110, A005117, A007947, A034444, A050320, A072047, A259936.
%K nonn
%O 1,5
%A _Gus Wiseman_, Sep 15 2019
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