A set of identities involving -D visible lattice points was discovered by Campbell (1994). Examples include
References
Campbell, G. B. ``Infinite Products Over Visible Lattice Points.'' Internat. J. Math. Math. Sci. 17, 637-654, 1994.
Campbell, G. B. ``Visible Point Vector Identities.''
http://www.geocities.com/CapeCanaveral/Launchpad/9416/vpv.html.