Catalyzes the irreversible transfer of a propylamine group from the amino donor S-adenosylmethioninamine (decarboxy-AdoMet) to putrescine (1,4-diaminobutane) to yield spermidine. It has lower affinity and lower activity towards 1,3-diaminopropane, cadaverine (1,5-diaminopentane), agmatine, norspermidine and spermidine (in vitro). putrescine + S-adenosyl 3-(methylsulfanyl)propylamine = H(+) + S-methyl-5'-thioadenosine + spermidine Strongly inhibited by S-adenosyl-1,8-diamino-3-thiooctane. kcat is 0.77 sec(-1) for aminopropyltransferase activity with putrescine as substrate (at pH 7.5 and 37 degrees Celsius). kcat is 22.7 sec(-1) for aminopropyltransferase activity with putrescine as substrate (at pH 7.5 and 80 degrees Celsius). Optimum pH is 7.5. Optimum temperature is 90 degrees Celsius. Amine and polyamine biosynthesis; spermidine biosynthesis; spermidine from putrescine: step 1/1. Homotetramer. Belongs to the spermidine/spermine synthase family.