A063950 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 positive square < n.

0, 1, 3, 4, 5, 7, 9, 12, 13, 15, 17, 20, 21, 25, 28, 33, 36, 41, 45, 49, 52, 57, 60, 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: 1

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

r[n_, x_] := Reduce[n == x^2 + y^2 + z^2 + t^2, {y, z, t}, Integers]; solQ[n_, x_] := r[n, x] =!= False; ok[0] = True; ok[n_] := And @@ (solQ[n, #] & ) /@ Range[1, Sqrt[n - 1]]; A063950 = Select[ Select[ Range[0, 4000], Mod[#, 4] != 2 &], If[ok[#], Print[#]; True, False] &](* Jean-François Alcover, May 15 2012 *)

Extensions

385 added by T. D. Noe, Apr 05 2007