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 A336737 #6 Aug 06 2020 23:29:08
%S A336737 1,1,1,2,1,2,1,2,2,2,1,3,1,2,2,3,1,3,1,3,2,2,1,4,2,2,2,3,1,5,1,2,2,2,
%T A336737 2,7,1,2,2,4,1,5,1,3,3,2,1,6,2,3,2,3,1,4,2,4,2,2,1,9,1,2,3,4,2,5,1,3,
%U A336737 2,5,1,9,1,2,3,3,2,5,1,6,3,2,1,9,2,2,2
%N A336737 Number of factorizations of n whose factors have pairwise intersecting prime signatures.
%C A336737 First differs from A327400 at a(72) = 9, A327400(72) = 10.
%C A336737 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
%e A336737 The a(n) factorizations for n = 2, 4, 12, 24, 30, 36, 60:
%e A336737 (2) (4) (12) (24) (30) (36) (60)
%e A336737 (2*2) (2*6) (2*12) (5*6) (4*9) (2*30)
%e A336737 (2*2*3) (2*2*6) (2*15) (6*6) (3*20)
%e A336737 (2*2*2*3) (3*10) (2*18) (5*12)
%e A336737 (2*3*5) (3*12) (6*10)
%e A336737 (2*3*6) (2*5*6)
%e A336737 (2*2*3*3) (2*2*15)
%e A336737 (2*3*10)
%e A336737 (2*2*3*5)
%t A336737 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A336737 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A336737 prisig[n_]:=If[n==1,{},Last/@FactorInteger[n]];
%t A336737 Table[Length[Select[facs[n],stableQ[#,Intersection[prisig[#1],prisig[#2]]=={}&]&]],{n,100}]
%Y A336737 A001055 counts factorizations.
%Y A336737 A118914 is sorted prime signature.
%Y A336737 A124010 is prime signature.
%Y A336737 A336736 counts factorizations with disjoint signatures.
%Y A336737 Cf. A003182, A051185, A305843, A305844, A305854, A306006, A319752, A319787, A319789, A321469, A336424.
%K A336737 nonn
%O A336737 1,4
%A A336737 _Gus Wiseman_, Aug 06 2020