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Number of non-constant 3-term geometric progressions with no term exceeding n.
3

%I #9 Oct 21 2017 16:21:05

%S 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 36,38,38,38,38,44,44,44,44,54,54,54,54,56,56,56,56,58,62,62,62,68,80,

%U 88,88,90,90,94,94,96,96,96,96,98,98,98,102,116,116,116,116,118,118,118

%N Number of non-constant 3-term geometric progressions with no term exceeding n.

%C In racetrack language, this is the number of trifectas in geometric progression in an n-horse race.

%C It appears that geometric progression like (k,0,0) are excluded. - _Stefan Steinerberger_, Nov 24 2007

%H 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.

%t 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 *)

%K nonn

%O 1,4

%A _Gerry Myerson_, Nov 21 2007

%E More terms from _Stefan Steinerberger_, Nov 24 2007