  Investigating star formation requires precise knowledge of the properties of
the dense molecular gas. The low metallicity and wide range of star formation
activity of the Large and Small Magellanic Clouds make them prime laboratories
to study how local physical conditions impact the dense gas reservoirs. The aim
of the Dense Gas Survey for the Magellanic Clouds (DeGaS-MC) project is to
expand our knowledge of the relation between dense gas properties and star
formation activity by targeting the LMC and SMC observed in the HCO+(2-1) and
HCN(2-1) transitions. We carried out a pointing survey toward 30 LMC and SMC
molecular clouds using the SEPIA180 instrument installed on the APEX telescope
and a follow-up mapping campaign in 13 star-forming regions. This first paper
provides line characteristic catalogs and integrated line-intensity maps of the
sources. HCO+(2-1) is detected in 20 and HCN(2-1) in 8 of the 29 pointings
observed. The dense gas velocity pattern follows the line-of-sight velocity
field derived from the stellar population. The HCN emission is less extended
than the HCO+ emission. The HCO+(2-1)/HCN(2-1) brightness temperature ratios
range from 1 to 7, which is consistent with the large ratios commonly observed
in low-metallicity environments. A larger number of young stellar objects are
found at high HCO+ intensities and lower HCO+/HCN flux ratios, and thus toward
denser lines of sight. The dense gas luminosities correlate with the star
formation rate traced by the total infrared luminosity over the two orders of
magnitude covered by our observations, although substantial region-to-region
variations are observed.
