  We observe the emission of bunches of $k \geqslant 1$ photons by a circuit
made of a microwave resonator in series with a voltage-biased tunable Josephson
junction. The bunches are emitted at specific values $V_k$ 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~k$\Omega$ 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 $E_J$. We also measure the second
order correlation function of the radiated microwave to determine its Fano
factor $F_k$, which in the low $E_J$ limit, confirms with $F_k=k$ the emission
of $k$ photon bunches. At larger $E_J$, a more complex behavior is observed in
quantitative agreement with numerical simulations.
