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 A186287 #21 Mar 28 2015 16:28:31
%S A186287 1,1,2,1,1,6,3,3,2,1,1,2,1,1,30,15,15,10,5,5,10,5,5,6,3,3,2,1,1,2,1,1,
%T A186287 6,3,3,2,1,1,2,1,1,105,105,105,35,35,35,35,35,35,21,21,21,7,7,7,7,7,7,
%U A186287 21,21,21,7,7,7,7,7,7,15,15,15,5,5,5,5,5,5,3,3,3,1,1,1,1,1,1,3,3,3
%N A186287 a(n) is the denominator of the rational number whose "factorization" into terms of A186285 has the balanced ternary representation corresponding to n.
%C A186287 Denominators from the ordering of positive rational numbers by increasing balanced ternary representation of the "factorization" of positive rational numbers into terms of A186285 (prime powers with a power of three as exponent).
%H A186287 Daniel Forgues, <a href="/A186287/b186287.txt">Table of n, a(n) for n = 0..9841</a>
%H A186287 OEIS Wiki, <a href="/wiki/Orderings_of_rational_numbers">Orderings of rational numbers</a>
%F A186287 The balanced ternary representation of n
%F A186287 n = Sum(i=0..1+floor(log_3(2|n|)) n_i * 3^i, n_i in {-1,0,1},
%F A186287 is taken as the representation of the "factorization" of the positive rational number c(n)/d(n) into terms from A186285
%F A186287 c(n)/d(n) = Prod(i=0..1+floor(log_3(2|n|)) (A186285(i+1))^(n_i), where A186285(i+1) is the (i+1)th prime power with exponent being a power of 3. Then a(n) is the denominator, i.e., d(n).
%e A186287 The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
%e A186287 n BalTern A186286/A186287 (in reduced form)
%e A186287 0 0 Empty product = 1 = 1/1, a(n) = 1
%e A186287 1 1 2 = 2/1, a(n) = 1
%e A186287 2 12 3*(1/2) = 3/2, a(n) = 2
%e A186287 3 10 3 = 3/1, a(n) = 1
%e A186287 4 11 3*2 = 6 = 6/1, a(n) = 1
%e A186287 5 122 5*(1/3)*(1/2) = 5/6, a(n) = 6
%e A186287 6 120 5*(1/3) = 5/3, a(n) = 3
%e A186287 7 121 5*(1/3)*2 = 10/3, a(n) = 3
%e A186287 ... ...
%e A186287 41 12222 8*(1/7)*(1/5)*(1/3)*(1/2) = 8/210 = 4/105, a(n) = 105
%Y A186287 Cf. A186285, A186286, A185169, A052330.
%K A186287 nonn,frac
%O A186287 0,3
%A A186287 _Daniel Forgues_, Feb 17 2011