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

1,4

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

Table of n, a(n) for n=1..70.

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

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 *)

Crossrefs

Sequence in context: A244459 A064849 A269302 * A162799 A034585 A171869

Adjacent sequences: A132186 A132187 A132188 * A132190 A132191 A132192

Keyword

nonn

Author

Gerry Myerson, Nov 21 2007

Extensions

More terms from Stefan Steinerberger, Nov 24 2007

Status

approved