Recently I have been puzzling again, over the Dharwadker-Khachatryan sum rule
mH = mW + 1/2 mZ
The problem being that it works quite well; but theory tends to favor relations among the squares of these masses (e.g. the "Veltman condition").
The primary purpose of this post is just to observe that you can get such a relation by squaring both sides of the D-K equation.
You do also get a term mW mZ. Perhaps it could result from a geometric mean, as in Torrente-Lujan.
Another simple thing that I want to observe, is that you might obtain something like D-K, by taking the square root of a Veltman-like sum rule. In other words, it could be approximately true, not by chance and not because it is directly implied by a fundamental theory, but as an algebraic side-effect of the truly fundamental relationship.
(The same applies to the Lopez-Castro - Pestieau - Garces-Doz sum rule, previously discussed here, which does involve masses squared, and therefore even more closely resembles Veltman's condition.)
P.S. Dharwadker also has a numerology for the ratio baryonic matter : dark matter : dark energy, which he deduces to be 1:5:18.