  In the presence of strong clustering, low-resolution surveys measure the
summed contributions of groups of sources within the beam. The counts of bright
intensity peaks are therefore shifted to higher flux levels compared to the
counts of individual sources detected with high-resolution instruments. If the
beam-width corresponds a sizable fraction of the clustering size, as in the
case of Planck/HFI, one actually detects the fluxes of clumps of sources. We
argue that the distribution of clump luminosities can be modelled in terms of
the two- and three-point correlation functions, and apply our formalism to the
Planck/HFI 850 micron surveys. The effect on counts is found to be large and
sensitive also to the evolution of the three-point correlation function; in the
extreme case that the latter function is redshift-independent, the source
confusion due to clustering keeps being important above the canonical 5*sigma
detection limit. Detailed simulations confirm the reliability of our approach.
As the ratio of the beam-width to the clustering angular size decreases, the
observed fluxes approach those of the brightest sources in the beam and the
clump formalism no longer applies. However, simulations show that also in the
case of the Herschel/SPIRE 500 micron survey the enhancement of the bright
source counts due to clustering is important.
