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%I #18 May 22 2016 00:13:53
%S 85,130,340,520,1360,2080,5440,8320,21760,33280,87040,133120,348160,
%T 532480,1392640,2129920,5570560,8519680,22282240,34078720,89128960,
%U 136314880,356515840,545259520,1426063360,2181038080,5704253440,8724152320
%N Values of A007692(n) that are not of the form x^2 + y^2 + z^2 where x, y, z are nonzero integers.
%C 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.
%C For more details see A051952.
%e 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.
%e 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.
%e 340 is a term because 340 = 4*85 and 85 is a term.
%t 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 *)
%Y Cf. A000408, A004214, A007692, A051952.
%K nonn
%O 1,1
%A _Altug Alkan_, May 16 2016
%E a(14)-a(28) from _Giovanni Resta_, May 16 2016
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