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A356181 a(n) = A054406(A001951(n)).

%I A356181 #7 Mar 23 2025 18:39:38
%S A356181 2,4,9,11,16,18,21,26,28,33,35,37,42,44,49,52,56,59,61,66,68,73,75,78,
%T A356181 82,85,89,92,97,99,101,106,108,113,115,118,123,125,130,132,134,139,
%U A356181 141,146,149,153,156,158,163,165,170,172,175,179,182,186,189,194
%N A356181 a(n) = A054406(A001951(n)).
%C A356181 This is the second of four sequences that partition the positive integers. See A356180.
%e A356181 (1)  v o u = (1, 3, 6, 8, 12, 13, 15, 19, 20, 24, 25, 27, 31, 32, ...) = A356180
%e A356181 (2)  v' o u = (2, 4, 9, 11, 16, 18, 21, 26, 28, 33, 35, 37, 42, 44, ...) = A356181
%e A356181 (3)  v o u' = (5, 10, 17, 22, 29, 34, 39, 46, 51, 58, 64, 69, 76, ...) = A356182
%e A356181 (4)  v' o u' = (7, 14, 23, 30, 40, 47, 54, 63, 70, 80, 87, 94, 104, ...) = A356183
%t A356181 z = 800; zz = 100;
%t A356181 u = Table[Floor[n*Sqrt[2]], {n, 1, z}];  (* A001951 *)
%t A356181 u1 = Complement[Range[Max[u]], u];       (* A001952 *)
%t A356181 v = Table[Floor[n*Sqrt[3]], {n, 1, z}];  (* A022838 *)
%t A356181 v1 = Complement[Range[Max[v]], v];  (* A054406 *)
%t A356181 Table[v[[u[[n]]]], {n, 1, zz}]      (* A356180 *)
%t A356181 Table[v1[[u[[n]]]], {n, 1, zz}]     (* A356181 *)
%t A356181 Table[v[[u1[[n]]]], {n, 1, zz}]     (* A356182 *)
%t A356181 Table[v1[[u1[[n]]]], {n, 1, zz}]    (* A356183 *)
%Y A356181 Cf. A001951, A001952, A022838, A054406, A346308 (intersections), A356088 (reverse composites), A356180, A356182, A356183.
%K A356181 nonn,easy
%O A356181 1,1
%A A356181 _Clark Kimberling_, Aug 24 2022