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A198772 Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y. 9
0, 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 52, 57, 61, 63, 64, 67, 73, 75, 76, 79, 81, 84, 93, 97, 100, 103, 108, 109, 111, 112, 117, 121, 124, 127, 129, 139, 144, 148, 151, 156, 157, 163, 171, 172, 175, 181, 183, 189, 192, 193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

A088534(a(n)) = 1.

a(n) = A034022(n) for n <= 32.

EXAMPLE

a(20) = 48 = 4^2 + 4*4 + 4^2, A088534(48) = 1;

a(21) = 52 = 2^2 + 2*6 + 6^2, A088534(52) = 1.

MATHEMATICA

amax = 200; xmax = Sqrt[amax] // Ceiling; Clear[f]; f[_] = 0; Do[q = x^2 + x y + y^2; f[q] = f[q] + 1, {x, 0, xmax}, {y, x, xmax}];

A198772 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 1&] (* Jean-Fran├žois Alcover, Jun 21 2018 *)

PROG

(Haskell)

a198772 n = a198772_list !! (n-1)

a198772_list = filter ((== 1) . a088534) a003136_list

(Julia)

function isA198772(n)

    M = Int(round(2*sqrt(n/3)))

    count = 0

    for y in 0:M, x in 0:y

        n == x^2 + y^2 + x*y && (count += 1)

        count == 2 && break

    end

    return count == 1

end

A198772list(upto) = [n for n in 0:upto if isA198772(n)]

A198772list(193) |> println # Peter Luschny, Mar 17 2018

CROSSREFS

Subsequence of Loeschian numbers A003136.

Complement of A118886 with respect to A003136.

Cf. A198773, A198774, A198775.

Sequence in context: A003136 A326421 A034022 * A185256 A070992 A246514

Adjacent sequences:  A198769 A198770 A198771 * A198773 A198774 A198775

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 30 2011

STATUS

approved

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)