A094942 Numbers having a unique partition into three squares.

0, 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 19, 20, 21, 22, 24, 30, 32, 35, 37, 40, 42, 43, 44, 46, 48, 52, 56, 58, 64, 67, 70, 76, 78, 80, 84, 88, 91, 93, 96, 115, 120, 128, 133, 140, 142, 148, 160, 163, 168, 172, 176, 184, 190, 192, 208, 224, 232, 235

Offset: 1

Author

T. D. Noe, May 24 2004

Keywords

• nonn

Comments

Note that squares are allowed to be zero.

From Wolfdieter Lang, Apr 09 2013: (Start)

These are the numbers for which A000164(a(n)) = 1.

a(n) is the n-th largest number which has a representation as a sum of three squares (square 0 allowed), in exactly one way, if neither the order of terms nor the signs of the numbers to be squared are taken into account. The multiplicity with order and signs taken into account are A005875(a(n)).

These numbers are a proper subset of A000378.

(End)

Note that all these numbers are 4^k * A094739(n) for some k >= 0. - T. D. Noe, Nov 08 2013

Examples

			From _Wolfdieter Lang_, Apr 09 2013 (Start)
a(1) = 0 because 0 = 0^2 + 0^2 + 0^2 and 0 is the first number m with A000164(m)=1.
a(8) = 8 = 0^2 + 2^2 + 2^2, the 8th largest number m for which A000164(m) is 1.
(End)
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A025321 (numbers having a unique partition into three positive squares), A094739 (primitive n having a unique partition into three squares).

Cf. A000164, A005875, A000378, A224442 (two ways), A224443 (three ways).

Programs

Mathematica

lim=25; nLst=Table[0, {lim^2}]; Do[n=a^2+b^2+c^2; If[n>0 && nRay Chandler, Oct 31 2019 *)

Formula

The sequence gives the increasingly ordered members of the set {m integer | A000164(m) = 1, m >= 0}.

Extensions

0 added by T. D. Noe, Apr 09 2013