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.
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