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A183300
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Positive integers not of the form 2n^2.
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4
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1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86
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OFFSET
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1,2
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COMMENTS
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Integers whose number of even divisors (A183063) is even (for a proof, see A001105, the complement of this sequence), hence odd numbers (A005408) are a subsequence. - Bernard Schott, Sep 15 2021
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LINKS
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FORMULA
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EXAMPLE
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10 is in the sequence since 2*2^2=8 < 10 < 2*3^2=18.
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MAPLE
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MATHEMATICA
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a = 2; b = 0;
F[n_] := a*n^2 + b*n;
R[n_] := (n/a + ((b - 1)/(2a))^2)^(1/2);
G[n_] := n - 1 + Ceiling[R[n] - (b - 1)/(2a)];
Table[F[n], {n, 60}]
r[n_] := Reduce[n == 2*k^2, k, Integers]; Select[Range[100], r[#] === False &] (* Jean-François Alcover, Dec 17 2013 *)
max = 100; Complement[Range[max], 2 Range[Ceiling[Sqrt[max/2]]]^2] (* Alonso del Arte, Dec 17 2013 *)
Module[{nn=10, f}, Complement[Range[2nn^2], 2Range[nn]^2]] (* Harvey P. Dale, Sep 06 2023 *)
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PROG
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(Magma) [n: n in [0..100] | not IsSquare(n/2)]; // Bruno Berselli, Dec 17 2013
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CROSSREFS
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Cf. A001105 (number of even divisors is odd), A028982 (number of odd divisors is odd), A028983 (number of odd divisors is even), this sequence (number of even divisors is even).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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