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 A130724 #16 Oct 07 2023 05:06:26
%S A130724 0,3,6,1,12,15,2,21,24,3,30,33,4,39,42,5,48,51,6,57,60,7,66,69,8,75,
%T A130724 78,9,84,87,10,93,96,11,102,105,12,111,114,13,120,123,14,129,132,15,
%U A130724 138,141,16,147,150,17,156,159,18,165,168,19,174,177,20,183,186
%N A130724 a(n) = lcm(n,3) / gcd(n,3).
%H A130724 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A130724 a(n) = A109044(n) / A109007(n).
%F A130724 From _Wesley Ivan Hurt_, Jul 24 2016: (Start)
%F A130724 G.f.: x*(3 + 6*x + x^2 + 6*x^3 + 3*x^4)/(x^3 - 1)^2.
%F A130724 a(n) = 2*a(n-3) - a(n-6) for n>5.
%F A130724 a(n) = 27*n/(5 + 4*cos(2*n*Pi/3))^2.
%F A130724 If n mod 3 = 0, then n/3, else 3*n.
%F A130724 a(n) = lcm(numerator(n/3), denominator(n/3)). (End)
%F A130724 Sum_{k=1..n} a(k) ~ (19/18)*n^2. - _Amiram Eldar_, Oct 07 2023
%e A130724 a(7) = 21 because lcm(3,7) = 21, gcd(3,7) = 1 and 21/1 = 21.
%p A130724 A130724:=n->lcm(n,3)/gcd(n,3): seq(A130724(n), n=0..100); # _Wesley Ivan Hurt_, Jul 24 2016
%t A130724 LCM[3,#]/GCD[3,#]&/@Range[0,70] (* _Harvey P. Dale_, May 16 2013 *)
%o A130724 (Magma) [Lcm(n,3)/Gcd(n,3) : n in [0..100]]; // _Wesley Ivan Hurt_, Jul 24 2016
%Y A130724 Cf. A109007, A109044.
%K A130724 easy,nonn
%O A130724 0,2
%A A130724 _W. Neville Holmes_, Jul 04 2007
%E A130724 Corrected and extended by _Harvey P. Dale_, May 16 2013