Catalyzes the irreversible transfer of a propylamine group from the amino donor S-adenosylmethioninamine (decarboxy-AdoMet) to putrescine (1,4-diaminobutane) to yield spermidine. putrescine + S-adenosyl 3-(methylsulfanyl)propylamine = H(+) + S-methyl-5'-thioadenosine + spermidine Amine and polyamine biosynthesis; spermidine biosynthesis; spermidine from putrescine: step 1/1. Homodimer or homotetramer. Belongs to the spermidine/spermine synthase family. Extended N-terminus.