Equation to inverse scale of child bone to maintain world scale?

I’m trying to set it up so when I change the scale of my parent bone, it inverses the children of that bone so that while the scale of my parent bone increases/decreases, it’s children stay at the same world scale. What would the equation be to inverse the scale correctly? Any help is appreciated.

I think this should work but haven’t tried it. Set your scale factor as a variable. Eg. Desired root scale is 1.2 scaleFactor = 0.2. Then scale root bone by 1+scaleFactor. Then loop through child bones and scale by 1- scaleFactor. I think this should keep a relative scale, However I have had a drink or 2 tonight.