%I #7 Sep 23 2019 13:43:57
%S 0,0,0,0,0,1,0,0,0,1,0,2,0,1,1,0,0,2,0,2,1,1,0,2,0,1,0,2,0,4,0,0,1,1,
%T 1,4,0,1,1,2,0,4,0,2,2,1,0,3,0,2,1,2,0,2,1,2,1,1,0,6,0,1,2,0,1,4,0,2,
%U 1,4,0,4,0,1,2,2,1,4,0,3,0,1,0,6,1,1,1
%N Number of non-constant factorizations of n whose distinct factors are pairwise coprime.
%F a(n) = A327399(n) - A089723(n).
%e The factorizations of 6, 12, 30, 48, 60, 180, and 210:
%e (2*3) (3*4) (5*6) (3*16) (3*20) (4*45) (3*70)
%e (2*2*3) (2*15) (3*4*4) (4*15) (5*36) (5*42)
%e (3*10) (2*2*2*2*3) (5*12) (9*20) (6*35)
%e (2*3*5) (3*4*5) (4*5*9) (7*30)
%e (2*2*15) (5*6*6) (10*21)
%e (2*2*3*5) (2*2*45) (14*15)
%e (3*3*20) (2*105)
%e (2*2*5*9) (5*6*7)
%e (3*3*4*5) (2*3*35)
%e (2*2*3*3*5) (2*5*21)
%e (2*7*15)
%e (3*5*14)
%e (3*7*10)
%e (2*3*5*7)
%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t Table[Length[Select[facs[n],CoprimeQ@@Union[#]&]],{n,100}]
%Y Factorizations that are constant or whose distinct parts are pairwise coprime are counted by A327399.
%Y Numbers with pairwise coprime distinct prime indices are A304711.
%Y Cf. A001055, A089723, A281116, A318721, A302569, A319269, A327407, A327517.
%K nonn
%O 1,12
%A _Gus Wiseman_, Sep 22 2019