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%I #25 Jul 22 2019 14:43:38
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,31,32,33,34,35,36,37,38,40,41,42,43,44,45,47,48,49,52,53,56,
%U 58,59,60,61,64,67,68,69,72,73,76,77,80,83,89,92,96,97,101,104,108,112,124,128,136,188,224
%N Numbers that are not the sum of 5 distinct squares.
%H Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa67/aa6745.pdf">Sums of distinct squares</a>, Acta Arith. 67 (1994), 349-380.
%H E. M. Wright, <a href="https://doi.org/10.1093/qmath/os-4.1.37">The representation of a number as a sum of five or more squares</a>, Quart. J. Math. Oxford Ser. 4 (1933), 37-51.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%t nn=10000; t=Table[0,{nn}]; lim=Floor[Sqrt[nn]]; sq=Table[i^2, {i,0,lim}]; lim=lim+1; Do[n=sq[[i1]]+sq[[i2]]+sq[[i3]]+sq[[i4]]+sq[[i5]]; If[n<=nn, t[[n]]++ ], {i1,lim}, {i2,i1+1,lim}, {i3,i2+1,lim}, {i4,i3+1,lim}, {i5,i4+1,lim}]; Flatten[Position[t,0]] (* _T. D. Noe_, Jul 24 2006 *)
%t j[{a_, b_, c_, d_, e_}] := If[0 <= a < b < c < d < e, a^2 + b^2 + c^2 + d^2 + e^2, False]; Union[ Complement[Range[500], DeleteCases[ Flatten[Map[j, PowersRepresentations[ #, 5, 2]] & /@ Range[500]], False]]] (* _Ant King_, Sep 30 2010 *)
%Y Cf. A120951.
%K nonn,fini,full
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Franklin T. Adams-Watters_, Jul 18 2006
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