

A094740


Numbers n such that 4^k n, for k >= 0, are numbers having a unique partition into three positive squares.


4



3, 6, 9, 11, 14, 17, 18, 19, 21, 22, 26, 29, 30, 34, 35, 42, 43, 45, 46, 49, 50, 53, 61, 65, 67, 70, 73, 78, 82, 91, 93, 97, 106, 109, 115, 133, 142, 145, 157, 163, 169, 190, 193, 202, 205, 235, 253, 265, 277, 298, 397, 403, 427, 442, 445, 505, 793
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OFFSET

1,1


COMMENTS

It is conjectured that this sequence is complete.


LINKS



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, Sqrt[lim^2a^2]}, {c, b, Sqrt[lim^2a^2b^2]}]; Select[Flatten[Position[nLst, 1]], Mod[ #, 4]>0&]


CROSSREFS

Cf. A094739 (n having a unique partition into three squares).


KEYWORD

nonn


AUTHOR



STATUS

approved



