We present a study of star-forming galaxies (SFGs) with pseudobulges (bulges with S\'ersic index n < 2) in a local close major-merger galaxy pair sample (H-KPAIR). With data from new aperture photometries in the optical and near-infrared bands (aperture size of 7\;kpc) and from the literature, we find that the mean Age of central stellar populations in Spirals with pseudobulges is consistent with that of disky galaxies and is nearly constant against the bulge-to-total ratio (B/T). Paired Spirals have a slightly lower fraction of pure disk galaxies (B/T ≤ 0.1) than their counterparts in the control sample. Compared to SFGs with classical bulges, those with pseudobulges have a higher (>2\;σ) mean of specific star formation rate (sSFR) enhancement (sSFRₑₙₕ = 0.33±0.07 vs sSFRₑₙₕ = 0.12±0.06) and broader scatter (by ~ 1\;dex). The eight SFGs that have the highest sSFRₑₙₕ in the sample all have pseudobulges. A majority (69%) of paired SFGs with strong enhancement (having sSFR more than 5 times the median of the control galaxies) have pseudobulges. The Spitzer data show that the pseudobulges in these galaxies are tightly linked to nuclear/circum-nuclear starbursts. Pseudobulge SFGs in S+S and in S+E pairs have significantly (>3\;σ) different sSFR enhancement, with the means of sSFRₑₙₕ = 0.45±0.08 and -0.04±0.11, respectively. We find a decrease in the sSFR enhancements with the density of the environment for SFGs with pseudobulges. Since a high fraction (5/11) of pseudobulge SFGs in S+E pairs are in rich groups/clusters (local density N1Mpc ≥ 7), the dense environment might be the cause for their low sSFRₑₙₕ.
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