A132189 Number of non-constant 3-term geometric progressions with no term exceeding n.

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, 36, 38, 38, 38, 38, 44, 44, 44, 44, 54, 54, 54, 54, 56, 56, 56, 56, 58, 62, 62, 62, 68, 80, 88, 88, 90, 90, 94, 94, 96, 96, 96, 96, 98, 98, 98, 102, 116, 116, 116, 116, 118, 118, 118

Offset: 1

Author

Gerry Myerson, Nov 21 2007

Keywords

• nonn

Comments

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

It appears that geometric progression like (k,0,0) are excluded. - Stefan Steinerberger, Nov 24 2007

Links

• Gerry Myerson, Trifectas in Geometric Progression, Australian Mathematical Society Gazette, Volume 35 Number 3 July 2008 pp. 189-194.

Crossrefs

Cf. A132345.

Programs

Mathematica

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 *)

Formula

a(n) = 2 * A132345(n). - Alois P. Heinz, Jun 08 2025

Extensions

More terms from Stefan Steinerberger, Nov 24 2007