specific values Vk of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly k photons in the resonator. The latter is a micro-fabricated spiral coil which resonates and leaks photons at 4.4~GHz in a measurement line. Its characteristic impedance of 1.97~kΩ is high enough to reach a strong junction-resonator coupling and a bright emission of the k-photon bunches. We show that a RWA treatment of the system accounts quantitatively for the observed radiation intensity, from k=1 to 6, and over three orders of magnitude when varying the Josephson energy EJ. We also measure the second order correlation function of the radiated microwave to determine its Fano factor Fk, which in the low EJ limit, confirms with Fk=k the emission of k photon bunches. At larger EJ, a more complex behavior is observed in quantitative agreement with numerical simulations.