Minimum amount of colors preventing an equilateral uniformly colored subtriangle
Just an extended comment:

You can take a look to the approach used by Steinbach and Posthoff to find the 4-coloring of a 18x18 (and 12x21) grid without monochromatic rectangles:

Bernd Steinbach and Christian Posthoff, Solution of the Last Open Four-Colored Rectangle-free Grid an Extremely Complex Multiple-Valued Problem. In Proceedings of the 2013 IEEE 43rd International Symposium on Multiple-Valued Logic (ISMVL '13)

As proved by Gasarch et al. given a partial $c$-coloring of an arbitrary $n \times m$ rectangle, it is NP-complete to decide if the coloring can be extended to the whole rectangle without monochromatic rectangles: Daniel Apon, William Gasarch, Kevin Lawler, An NP-Complete Problem in Grid Coloring. 
So there are high chances that the problem is NP-complete even for equilateral triangles .... I think it would be a nice result to prove it.

Just a side note: I spent weeks of CPU cycles on the monochromatic rectangle-free 4-coloring problem but I started from a wrong partial result (a wrong previous analysis that restricted the number of possible 1-color sub-configurations) and I used the STP constraint solver; you can achieve great improvements if you add constraints that break symmetries (e.g. an ordering on the coloring of a side of the triangle) and try to make an analysis of the possible configurations using only 1-color.

EDIT: this is the result of an STP program for n=19 (~ 1 min.)