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Context. Evidence that the chemical characteristics around low- and high-mass protostars are similar has been found: notably, a variety of carbon-chain species and complex organic molecules (COMs) form around both types. On the other hand, the chemical compositions around intermediate-mass (IM) protostars (2M_⊙<m_*< 8M_⊙) have not been studied with large samples. In particular, it is unclear the extent to which carbon-chain species form around them. Aims. We aim to obtain the chemical compositions of a sample of IM protostars, focusing particularly on carbon-chain species. We also aim to derive the rotational temperatures of HC₅N to confirm whether carbon-chain species are formed in the warm gas around these stars. Methods. We conducted Q-band (31.5–50 GHz) line survey observations toward 11 mainly IM protostars with the Yebes 40 m radio telescope. The target protostars were selected from a subsample of the source list of the SOFIA Massive Star Formation project. Assuming local thermodynamic equilibrium, we derived the column densities of the detected molecules and the rotational temperatures of HC₅N and CH₃OH. Results. Nine carbon-chain species (HC₃N, HC₅N, C₃H, C₄Hlinear-H₂CCC,cyclic-C₃H₂, CCS, C₃S, and CH₃CCH), three COMs (CH₃OH, CH₃CHO, and CH₃CN), H₂CCO, HNCO, and four simple sulfur-bearing species (¹³CS, C³⁴S, HCS⁺, and H₂CS) are detected. The rotational temperatures of HC₅N are derived to be ~20–30 K in three IM protostars (Cepheus E, HH288, and IRAS 20293+3952). The rotational temperatures of CH₃OH are derived in five IM sources and found to be similar to those of HC₅N. Conclusions. The rotational temperatures of HC₅N around the three IM protostars are very similar to those around low- and high-mass protostars. These results indicate that carbon-chain molecules are formed in lukewarm gas (~20–30 K) around IM protostars via the warm carbon-chain chemistry process. Thus, carbon-chain formation occurs ubiquitously in the warm gas around protostars across a wide range of stellar masses. Carbon-chain molecules and COMs coexist around most of the target IM protostars, which is similar to the situation for low- and high-mass protostars. In summary, the chemical characteristics around protostars are the same in the low-, intermediate- and high-mass regimes.