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A273123
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Values of A007692(n) that are not of the form x^2 + y^2 + z^2 where x, y, z are nonzero integers.
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0
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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