A Divisibility Property of Primitive Chord Moments

For integers n ≥ 2, we consider an integer-valued expression in Euler's totient and the second and fourth Jordan totients. Classical finite trigonometric sums identify it with a sum of squared differences of inverse squared chord lengths. An elementary congruence argument shows that its values are divisible by 576, and by 2880 except at n = 5. We determine the exact common divisors, the zero set, and the unique least positive value.