A273123 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000408, A004214, A007692, A051952.

Sequence in context: A161479 A027453 A259219 * A239527 A029471 A083750

Adjacent sequences: A273120 A273121 A273122 * A273124 A273125 A273126

KEYWORD

nonn

AUTHOR

Altug Alkan, May 16 2016

EXTENSIONS

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

STATUS

approved