A004438 Numbers that are not the sum of 5 distinct squares.

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, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 52, 53, 56, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Links

• Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy, Sums of distinct squares, Acta Arith. 67 (1994), 349-380.
• E. M. Wright, The representation of a number as a sum of five or more squares, Quart. J. Math. Oxford Ser. 4 (1933), 37-51.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A120951.

Programs

Mathematica

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 *)
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 *)

Extensions

More terms from Franklin T. Adams-Watters, Jul 18 2006