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We define an extension of the Ramanujan trigonometric function to arbitrarydimensions, and give the Dirichlet series generating function. The extensionwas first given by Eckford Cohen long ago. This links directly to visible pointvector identities, and possibly to lattice sums in Physics and Chemistrypresented by Baake et al. New generating functions and summations are givenhere, generalizing the Ramanujan function, Euler totient and the Jordan totientfunctions, based on visible lattice point ideas.

Ramanujan and Eckford Cohen totients from Visible Point Identities