Ordered factorizations with one level of parentheses indexed by prime signatures. A050354(A025487).

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =9a(5) =21a(6) =27a(7) =81a(8) =37a(9) =81a(10) =111a(11) =297a(12) =201a(13) =243a(14) =513a(15) =1053a(16) =945a(17) =729a(18) =2187a(19) =1317a(20) =3645a(21) =365a(22) =2745a(23) =4077a(24) =2187a(25) =8829a(26) =7209a(27) =12393a(28) =2433a(29) =13257