Number of ordered factorizations indexed by prime signatures: A074206(A025487).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =8a(6) =8a(7) =20a(8) =13a(9) =16a(10) =26a(11) =48a(12) =44a(13) =32a(14) =76a(15) =112a(16) =132a(17) =64a(18) =208a(19) =176a(20) =256a(21) =75a(22) =252a(23) =368a(24) =128a(25) =544a(26) =604a(27) =576a(28) =308a(29) =768