n!/pp, where pp is the largest perfect power (A001597) which divides n!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =3a(5) =15a(6) =5a(7) =35a(8) =70a(9) =70a(10) =7a(11) =77a(12) =231a(13) =3003a(14) =858a(15) =1430a(16) =1430a(17) =24310a(18) =12155a(19) =230945a(20) =46189a(21) =230945a(22) =176358a(23) =4056234a(24) =676039a(25) =676039a(26) =104006a(27) =312018a(28) =44574a(29) =1292646