Decreasing partition array based on the fractional parts of tan(n); see Comments.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =6a(5) =4a(6) =8a(7) =9a(8) =18a(9) =7a(10) =11a(11) =12a(12) =21a(13) =10a(14) =16a(15) =90a(16) =15a(17) =34a(18) =13a(19) =20a(20) =17a(21) =630a(22) =93a(23) =37a(24) =14a(25) =25a(26) =26a(27) =23a(28) =1120a(29) =445