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 A319138 #4 Sep 12 2018 15:10:57
%S A319138 0,1,1,0,1,2,1,0,0,2,1,4,1,2,2,0,1,4,1,4,2,2,1,8,0,2,0,4,1,18,1,0,2,2,
%T A319138 2,28,1,2,2,8,1,18,1,4,4,2,1,16,0,4,2,4,1,8,2,8,2,2,1,84,1,2,4,0,2,18,
%U A319138 1,4,2,18,1,112,1,2,4,4,2,18,1,16,0,2,1
%N A319138 Number of complete strict planar branching factorizations of n.
%C A319138 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. A strict planar branching factorization is complete if the leaves are all prime numbers.
%F A319138 a(prime^n) = A000007(n - 1).
%F A319138 a(product of n distinct primes) = A032037(n).
%e A319138 The a(12) = 4 trees: (2*(2*3)), (2*(3*2)), ((2*3)*2), ((3*2)*2).
%t A319138 ordfacs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@ordfacs[n/d],{d,Rest[Divisors[n]]}]]
%t A319138 sotfs[n_]:=Prepend[Join@@Table[Tuples[sotfs/@f],{f,Select[ordfacs[n],And[Length[#]>1,UnsameQ@@#]&]}],n];
%t A319138 Table[Length[Select[sotfs[n],FreeQ[#,_Integer?(!PrimeQ[#]&)]&]],{n,100}]
%Y A319138 Cf. A000108, A045778, A074206, A118376, A277130, A281113, A281118, A295279, A295281, A317144, A319122, A319123, A319136, A319137.
%K A319138 nonn
%O A319138 1,6
%A A319138 _Gus Wiseman_, Sep 11 2018