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%I #7 May 02 2018 09:24:32
%S 1,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,3,2,2,1,4,1,2,1,3,1,5,1,1,2,2,
%T 2,5,1,2,2,4,1,5,1,3,3,2,1,5,1,3,2,3,1,4,2,4,2,2,1,9,1,2,3,1,2,5,1,3,
%U 2,5,1,8,1,2,3,3,2,5,1,5,1,2,1,9,2,2,2
%N Number of factorizations of n using elements of A007916 (numbers that are not perfect powers).
%C First differs from A081707 at a(60) = 9, A081707(60) = 8.
%F Dirichlet g.f.: Product_{n in A007916} 1/(1 - n^s).
%e The a(60) = 9 factorizations are (2*2*3*5), (2*2*15), (2*3*10), (2*5*6), (2*30), (3*20), (5*12), (6*10), (60).
%t radQ[n_]:=Or[n===1,GCD@@FactorInteger[n][[All,2]]===1];
%t facsr[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facsr[n/d],Min@@#>=d&]],{d,Select[Rest[Divisors[n]],radQ]}]];
%t Table[Length[facsr[n]],{n,100}]
%Y Cf. A000837, A001055, A001597, A007716, A007916, A045778, A052409, A052410, A162247, A281113, A281116, A303708, A303709, A303710.
%K nonn
%O 1,6
%A _Gus Wiseman_, Apr 29 2018
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