[seqfan] A generalization

[Antreas Hatzipolakis]

The circle below has twelve points evenly spaced on its circumference. How
many triangles can you make by connecting the points with the following
property: the sum of the numbers on the vertices of the triangle created
has at least 3 factors greater than 1?

The answer is: 145

Reference:
http://www.artofproblemsolving.com/Forum/viewtopic.php?f=41&t=586846

How about if the points are n on the circumference?
(formula?)

Antreas