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%I #36 Apr 03 2023 10:36:09
%S 15,22,50,114,167,175,186,212,231,238,303,364,420,428,454
%N Numbers whose shortest representation as a sum of positive cubes requires exactly 8 cubes.
%C Wieferich proved that 167 is the unique prime in this sequence. - _Jonathan Vos Post_, Sep 23 2006
%D Joe Roberts, Lure of the Integers, entry 239.
%H Jan Bohman and Carl-Erik Froberg, <a href="http://dx.doi.org/10.1007/BF01934077">Numerical investigation of Waring's problem for cubes</a>, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
%H G. L. Honaker, Jr. and Chris Caldwell, et al., <a href="https://t5k.org/curios/page.php?short=167">A Prime Curios Page</a>.
%H K. S. McCurley, <a href="http://dx.doi.org/10.1016/0022-314X(84)90100-8">An effective seven-cube theorem</a>, J. Number Theory, 19 (1984), 176-183.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Warings Problem</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%t max = 500; nn = Union[(#*#).# & /@ Tuples[Range[0, 7], {7}]][[1 ;; max]]; Select[{#, PowersRepresentations[#, 8, 3]} & /@ Complement[Range[max], nn] , #[[2]] != {} &][[All, 1]] (* _Jean-François Alcover_, Jul 21 2011 *)
%Y Subsequence of A018888.
%K nonn,fini,full
%O 1,1
%A Anonymous
%E Corrected by Arlin Anderson.
%E Additional comments from _Jud McCranie_.
%E Edited by _N. J. A. Sloane_, Aug 10 2022
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