We explore the relationships between the 3.3 {mu}m polycyclic aromatic hydrocarbon (PAH) feature and active galactic nucleus (AGN) properties of a sample of 54 hard X-ray selected bright AGNs, including both Seyfert 1 and Seyfert 2 type objects, using the InfraRed Camera (IRC) on board the infrared astronomical satellite AKARI. The sample is selected from the 9-month Swift/BAT survey in the 14-195 keV band and all of them have measured X-ray spectra at $E lesssim 10$ keV. These X-ray spectra provide measurements of the neutral hydrogen column density ($N_{rm H}$) towards the AGNs. We use the 3.3 {mu}m PAH luminosity ($L_{rm 3.3{mu}m}$) as a proxy for star formation activity and hard X-ray luminosity ($L_{rm 14-195keV}$) as an indicator of the AGN activity. We search for possible difference of star-formation activity between type 1 (un-absorbed) and type 2 (absorbed) AGNs. We have made several statistical analyses taking the upper-limits of the PAH lines into account utilizing survival analysis methods. The results of our $log(L_{rm 14-195keV})$ versus $log(L_{rm 3.3{mu}m})$ regression shows a positive correlation and the slope for the type 1/unobscured AGNs is steeper than that of type 2/obscured AGNs at a $3sigma$ level. Also our analysis show that the circum-nuclear star-formation is more enhanced in type 2/absorbed AGNs than type 1/un-absorbed AGNs for low X-ray luminosity/low Eddington ratio AGNs, while there is no significant dependence of star-formation activities on the AGN type in the high X-ray luminosities/Eddington ratios.
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