Catalyzes the production of spermidine from putrescine and decarboxylated S-adenosylmethionine (dcSAM). Has a strong preference for putrescine as substrate, and has very low activity towards 1,3-diaminopropane. Has extremely low activity towards spermidine. putrescine + S-adenosyl 3-(methylsulfanyl)propylamine = H(+) + S-methyl-5'-thioadenosine + spermidine The activity is thought to be regulated mainly by the availability of decarboxylated S-adenosylmethionine. Amine and polyamine biosynthesis; spermidine biosynthesis; spermidine from putrescine: step 1/1. Homodimer or homotetramer. Belongs to the spermidine/spermine synthase family.