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%I #24 May 21 2022 14:04:58
%S 216,729,1728,5832,6859,8000,13824,15625,19683,21952,24389,27000,
%T 46656,54872,64000,68921,74088,85184,91125,97336,110592,125000,148877,
%U 157464,175616,185193,195112,216000,250047,287496,300763,328509,343000,357911,373248,421875
%N Cubes that are the sum of three distinct positive cubes.
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), pp. 130, 147.
%H Donovan Johnson, <a href="/A066890/b066890.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = (A023042(n))^3. - _Christian N. K. Anderson_, Aug 10 2014
%e 729 is included because it is 9^3 and 1^3 + 6^3 + 8^3 = 729.
%t maxCube = (m = 67)^3; Reap[ Do[ bmax = (maxCube - a^3)^(1/3) // Ceiling; Do[ cmax = (maxCube - b^3)^(1/3) // Ceiling; Do[ n = a^3 + b^3 + c^3; If[n <= maxCube, If[ IntegerQ[n^(1/3)], Sow[n]]], {c, b, cmax}], {b, a, bmax}], {a, 1, (maxCube - 2)^(1/3) // Ceiling}]][[2, 1]] // Flatten // Union (* _Jean-François Alcover_, Mar 07 2013 *)
%K nonn
%O 1,1
%A _Harvey P. Dale_, Jan 22 2002
%E Offset corrected by _Arkadiusz Wesolowski_, Aug 06 2012