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.
%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