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%I #9 Feb 01 2021 19:27:22
%S 9,65,91,217,243,341,513,539,637,855,1001,1027,1125,1343,1729,1755,
%T 1853,2071,2457,2745,2771,2869,3059,3087,3473,4075,4097,4123,4221,
%U 4439,4825,4941,5427,5833,5859,5957,6175,6293,6561,7163,7471,8001,8027,8029,8125,8343,8729
%N Numbers that are the sum of an odd cube s and an even cube t such that 0 < s < t.
%H Robert Israel, <a href="/A339997/b339997.txt">Table of n, a(n) for n = 1..10000</a>
%e 65 is in the sequence since 1^3 + 4^3 = 1 + 64 = 65, where 0 < 1 < 64.
%p N:= 10000: # for terms <= N
%p S:= {seq(seq(s^3 + t^3, s = 1 .. min(t,floor((N-t^3)^(1/3))),2), t = 2 .. floor(N^(1/3)),2)}:
%p sort(convert(S,list)); # _Robert Israel_, Dec 30 2020
%t Table[If[Sum[Mod[i, 2] Mod[n - i + 1, 2] (Floor[i^(1/3)] - Floor[(i - 1)^(1/3)]) (Floor[(n - i)^(1/3)] - Floor[(n - i - 1)^(1/3)]), {i, Floor[n/2]}] > 0, n, {}], {n, 1200}] // Flatten
%Y Cf. A010057.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Dec 25 2020