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%I #5 Jan 04 2019 17:33:38
%S 1,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,3,2,2,1,4,1,2,1,3,1,5,1,2,2,2,
%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 strict factorizations of n into factors > 1 such that no factor is a power of any other factor.
%e The a(60) = 9 factorizations:
%e (2*3*10), (2*5*6), (3*4*5),
%e (2*30), (3*20), (4*15), (5*12), (6*10),
%e (60).
%t strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t Table[Length[Select[strfacs[n],stableQ[#,IntegerQ[Log[#1,#2]]&]&]],{n,100}]
%Y Cf. A001597, A007916, A025147, A045778, A052410, A087897, A275972, A305150, A323054, A323086, A323090, A323091.
%K nonn
%O 1,6
%A _Gus Wiseman_, Jan 04 2019
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