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 A132189 #12 Jun 08 2025 14:49:14
%S A132189 0,0,0,2,2,2,2,4,8,8,8,10,10,10,10,16,16,20,20,22,22,22,22,24,32,32,
%T A132189 36,38,38,38,38,44,44,44,44,54,54,54,54,56,56,56,56,58,62,62,62,68,80,
%U A132189 88,88,90,90,94,94,96,96,96,96,98,98,98,102,116,116,116,116,118,118,118
%N A132189 Number of non-constant 3-term geometric progressions with no term exceeding n.
%C A132189 In racetrack language, this is the number of trifectas in geometric progression in an n-horse race.
%C A132189 It appears that geometric progression like (k,0,0) are excluded. - _Stefan Steinerberger_, Nov 24 2007
%H A132189 Gerry Myerson, <a href="http://www.austms.org.au/Gazette/2008/Jul08/TechPaperMyerson.pdf">Trifectas in Geometric Progression</a>, Australian Mathematical Society Gazette, Volume 35 Number 3 July 2008 pp. 189-194.
%F A132189 a(n) = 2 * A132345(n). - _Alois P. Heinz_, Jun 08 2025
%t A132189 a = {}; For[n = 1, n < 80, n++, c = 0; For[j = 1, j < n + 1, j++, For[h = 1, h < n + 1, h++, If[Not[h == j], If[IntegerQ[j*(h/j)^2], If[j*(h/j)^2 < n + 1, c++ ]]]]]; AppendTo[a, c]]; a (* _Stefan Steinerberger_, Nov 24 2007 *)
%Y A132189 Cf. A132345.
%K A132189 nonn
%O A132189 1,4
%A A132189 _Gerry Myerson_, Nov 21 2007
%E A132189 More terms from _Stefan Steinerberger_, Nov 24 2007