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A096017 Numbers n such that 4^k*n, for k >= 0, have a unique partition into three distinct positive squares. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 14:45 EDT 2021. Contains 346294 sequences. (Running on oeis4.)