A063953 Of course every number is the sum of 4 squares; these are the numbers not of the form 4m+2 such that the first square can be taken to be any square < n.

0, 1, 3, 4, 5, 9, 12, 13, 17, 20, 21, 25, 33, 36, 41, 45, 49, 52, 57, 65, 68, 73, 81, 84, 89, 97, 100, 105, 129, 132, 145, 153, 164, 169, 177, 180, 185, 196, 201, 209, 217, 225, 228, 257, 260, 273, 292, 297, 305, 313, 324, 329, 345, 353, 356, 385, 388, 420, 425, 433, 441, 481, 513, 516, 561, 580, 585, 609, 612, 676, 689, 697, 708, 713, 740, 804, 817, 825, 836, 868, 900, 945, 1028, 1092, 1188, 1220, 1252, 1316, 1380, 1412, 1540, 1700, 1732, 1764, 1924, 2052, 2244, 2340, 2436, 2756, 2788, 2852, 3268, 3300, 3780

Offset: 0

Author

N. J. A. Sloane, Sep 04 2001

Keywords

• nonn
• easy
• nice
• fini
• full

References

• J. H. Conway, personal communication, Aug 27, 2001.

Crossrefs

Cf. A063949-A063954.

Programs

Mathematica

ok[n_] := And @@ (Reduce[# + x^2 + y^2 + z^2 == n, {x, y, z}, Integers] =!= False & /@ Select[ Range[n-1], IntegerQ[Sqrt[#]]& ]); Reap[ Do[ If[Mod[n, 4] != 2 && ok[n], Print[n]; Sow[n]], {n, 0, 4000}]][[2, 1]] (* Jean-François Alcover, Jun 22 2012 *)