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 A319137 #6 Sep 12 2018 15:10:49
%S A319137 1,1,1,1,1,3,1,3,1,3,1,9,1,3,3,7,1,9,1,9,3,3,1,37,1,3,3,9,1,25,1,21,3,
%T A319137 3,3,57,1,3,3,37,1,25,1,9,9,3,1,161,1,9,3,9,1,37,3,37,3,3,1,153,1,3,9,
%U A319137 75,3,25,1,9,3,25,1,345,1,3,9,9,3,25,1,161
%N A319137 Number of strict planar branching factorizations of n.
%C A319137 A strict planar branching factorization of n is either the number n itself or a sequence of at least two strict planar branching factorizations, one of each factor in a strict ordered factorization of n.
%F A319137 a(prime^n) = A319123(n + 1).
%F A319137 a(product of n distinct primes) = A319122(n).
%e A319137 The a(12) = 9 trees:
%e A319137 12,
%e A319137 (2*6), (3*4), (4*3),(6*2),
%e A319137 (2*(2*3)), (2*(3*2)), ((2*3)*2), ((3*2)*2).
%t A319137 ordfacs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@ordfacs[n/d],{d,Rest[Divisors[n]]}]]
%t A319137 sotfs[n_]:=Prepend[Join@@Table[Tuples[sotfs/@f],{f,Select[ordfacs[n],And[Length[#]>1,UnsameQ@@#]&]}],n];
%t A319137 Table[Length[sotfs[n]],{n,100}]
%Y A319137 Cf. A000108, A001055, A045778, A074206, A118376, A277130, A281113, A281118, A292504, A295279, A295281, A317144, A319122, A319123, A319138.
%K A319137 nonn
%O A319137 1,6
%A A319137 _Gus Wiseman_, Sep 11 2018