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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327695 Number of non-constant factorizations of n whose distinct factors are pairwise coprime.

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%I A327695 #7 Sep 23 2019 13:43:57
%S A327695 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 A327695 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 A327695 1,4,0,4,0,1,2,2,1,4,0,3,0,1,0,6,1,1,1
%N A327695 Number of non-constant factorizations of n whose distinct factors are pairwise coprime.
%F A327695 a(n) = A327399(n) - A089723(n).
%e A327695 The factorizations of 6, 12, 30, 48, 60, 180, and 210:
%e A327695   (2*3)  (3*4)    (5*6)    (3*16)       (3*20)     (4*45)       (3*70)
%e A327695          (2*2*3)  (2*15)   (3*4*4)      (4*15)     (5*36)       (5*42)
%e A327695                   (3*10)   (2*2*2*2*3)  (5*12)     (9*20)       (6*35)
%e A327695                   (2*3*5)               (3*4*5)    (4*5*9)      (7*30)
%e A327695                                         (2*2*15)   (5*6*6)      (10*21)
%e A327695                                         (2*2*3*5)  (2*2*45)     (14*15)
%e A327695                                                    (3*3*20)     (2*105)
%e A327695                                                    (2*2*5*9)    (5*6*7)
%e A327695                                                    (3*3*4*5)    (2*3*35)
%e A327695                                                    (2*2*3*3*5)  (2*5*21)
%e A327695                                                                 (2*7*15)
%e A327695                                                                 (3*5*14)
%e A327695                                                                 (3*7*10)
%e A327695                                                                 (2*3*5*7)
%t A327695 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A327695 Table[Length[Select[facs[n],CoprimeQ@@Union[#]&]],{n,100}]
%Y A327695 Factorizations that are constant or whose distinct parts are pairwise coprime are counted by A327399.
%Y A327695 Numbers with pairwise coprime distinct prime indices are A304711.
%Y A327695 Cf. A001055, A089723, A281116, A318721, A302569, A319269, A327407, A327517.
%K A327695 nonn
%O A327695 1,12
%A A327695 _Gus Wiseman_, Sep 22 2019