a(n) is the first k such that A367566(k) = n, or -1 if no such k exists.

Terms

a(0) =252a(1) =1a(2) =2a(3) =-1a(4) =24a(5) =5a(6) =48a(7) =-1a(8) =-1a(9) =-1a(10) =450a(11) =-1a(12) =12a(13) =15a(14) =4a(15) =-1a(16) =1512a(17) =-1a(18) =18a(19) =-1a(20) =-1a(21) =45a(22) =8118a(23) =-1a(24) =-1a(25) =-1a(26) =-1a(27) =-1a(28) =840a(29) =-1