A096017 Numbers n such that 4^k*n, for k >= 0, have a unique partition into three distinct positive squares.

14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 59, 61, 65, 66, 70, 75, 78, 81, 83, 91, 93, 106, 107, 109, 113, 114, 115, 118, 121, 133, 137, 139, 142, 145, 147, 153, 157, 162, 169, 171, 178, 190, 198, 202, 205, 211, 214, 219, 226, 235, 243, 253, 258, 262, 265, 277, 283, 289, 291, 298, 307, 313, 323, 331, 337, 358, 363, 379, 387, 397, 403, 418, 427, 438, 442, 445, 457, 466, 498, 499, 505, 547, 562, 577, 603, 643, 723, 793, 883, 907, 1003, 1227, 1243, 1387, 1411, 1467, 1507

Offset

1,1

Comments

It is conjectured that this sequence is complete.

Links

Table of n, a(n) for n=1..102.

Example

793 is in this sequence because 793 = 6^2 + 9^2 + 26^2 is the unique partition of 793.

Mathematica

lim=100; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && n<lim^2, nLst[[n]]++ ], {a, lim}, {b, a+1, Sqrt[lim^2-a^2]}, {c, b+1, Sqrt[lim^2-a^2-b^2]}]; Select[Flatten[Position[nLst, 1]], Mod[ #, 4]>0&]

Crossrefs

Cf. A094739 (primitive n having a unique partition into three squares), A094740 (primitive n having a unique partition into three positive squares).

Sequence in context: A004432 A025339 A224771 * A274226 A324073 A006614

Adjacent sequences: A096014 A096015 A096016 * A096018 A096019 A096020

Keyword

nonn,fini,full

Author

T. D. Noe, Jun 15 2004

Status

approved