A273123 Values of A007692(n) that are not of the form x^2 + y^2 + z^2 where x, y, z are nonzero integers.

85, 130, 340, 520, 1360, 2080, 5440, 8320, 21760, 33280, 87040, 133120, 348160, 532480, 1392640, 2129920, 5570560, 8519680, 22282240, 34078720, 89128960, 136314880, 356515840, 545259520, 1426063360, 2181038080, 5704253440, 8724152320

Offset: 1

Author

Altug Alkan, May 16 2016

Keywords

• nonn

Comments

If n is in this sequence, then 4*n is also in this sequence. So 85*4^k and 130*4^k are terms of this sequence for all nonnegative values of k.

For more details see A051952.

Examples

			85 is a term because 85 = 2^2 + 9^2 = 6^2 + 7^2 and 85 = x^2 + y^2 + z^2 has no solution for nonzero integer values of x, y, z.
130 is a term because 130 = 3^2 + 11^2 = 7^2 + 9^2 and 130 = x^2 + y^2 + z^2 has no solution for nonzero integer values of x, y, z.
340 is a term because 340 = 4*85 and 85 is a term.
		

Crossrefs

Cf. A000408, A004214, A007692, A051952.

Programs

Mathematica

twoQ[n_] := 2 == Length@ Select[ PowersRepresentations[n, 2, 2], Times @@ # > 0 &, 2]; threeQ[n_] := {} != Quiet@ IntegerPartitions[n, {3}, Range[ Sqrt@ n]^2, 1]; Select[Range[10^5], twoQ[#] && ! threeQ[#] &] (* Giovanni Resta, May 16 2016 *)

Extensions

a(14)-a(28) from Giovanni Resta, May 16 2016