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a(n) is the sum of n addends nested as follows: floor(f(floor(f(...(n)...)))) where f(x) = x^(1/3).
1

%I #13 Oct 21 2019 02:26:43

%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,67,68,69,70,71,72,73

%N a(n) is the sum of n addends nested as follows: floor(f(floor(f(...(n)...)))) where f(x) = x^(1/3).

%C Its complement is 8, 28, 66, 128, 220, 348, 518, 519, 737, 1009, 1341, 1739, 2209, 2757, 3389, 4111, 4929, ..., .

%e For n=8, floor(8^(1/3))=2, and floor(floor(8^(1/3))^(1/3))=1 as do the remaining six terms, so a(8) = 2 + 7*1 = 9.

%t a[n_] := Plus @@ Rest@ NestList[ Floor[#^(1/3)] &, n, n]; Array[a, 60]

%Y Cf. A181092.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Nov 15 2012