  We analyse the $n$-dimensional superintegrable Kepler-Coulomb system with
non-central terms. We find a novel underlying chain structure of quadratic
algebras formed by the integrals of motion. We identify the elements for each
sub-structure and obtain the algebra relations satisfied by them and the
corresponding Casimir operators. These quadratic sub-algebras are realized in
terms of a chain of deformed oscillators with factorized structure functions.
We construct the finite-dimensional unitary representations of the deformed
oscillators, and give an algebraic derivation of the energy spectrum of the
superintegrable system.
