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A057102 a(n) = 4 * A073120(n). 13
24, 96, 120, 240, 336, 384, 480, 720, 840, 960, 1320, 1344, 1536, 1920, 1944, 2016, 2184, 2520, 2880, 3360, 3696, 3840, 3960, 4896, 5280, 5376, 5544, 6144, 6240, 6840, 6864, 7680, 7776, 8064, 8736, 9240, 9360, 9720, 10080, 10296, 10920, 11520, 12144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence was originally described as the list of "congrua". But that name more properly refers to A256418.

Numbers of the form (4(x^3y-xy^3) (where x,y are integers and x>=y). Squares of these numbers are of the form N^4-K^2 (where N belongs to A135786 and K to A135789 or A135790). Proof uses identity: (4(x^3y-xy^3))^2=(x^2+y^2)^4-(x^4 - 6x^2 y^2 + y^4)^2. - Artur Jasinski, Nov 29 2007, Nov 14 2008

LINKS

Table of n, a(n) for n=1..43.

MAPLE

N:= 10^5: # to get all terms <= N

select(`<=`, {seq(seq(4*(x^3*y-x*y^3), y=1..x-1), x=1..floor(sqrt(N/4+1)))}, N);

# If using Maple 11 or earlier, uncomment the following line

# sort(convert(%, list)); # Robert Israel, Apr 06 2015

MATHEMATICA

a = {}; Do[Do[w = 4x^3y - 4x y^3; If[w > 0 && w < 10000, AppendTo[a, w]], {x, y, 1000}], {y, 1, 1000}]; Union[a] (* Artur Jasinski, Nov 29 2007 *)

CROSSREFS

Cf. A073120, A256418.

Sequence in context: A103251 A256418 A198387 * A057103 A055669 A209432

Adjacent sequences:  A057099 A057100 A057101 * A057103 A057104 A057105

KEYWORD

nonn

AUTHOR

Henry Bottomley, Aug 02 2000

EXTENSIONS

Edited by N. J. A. Sloane, Apr 06 2015 at the suggestion of Robert Israel, Apr 03 2015

STATUS

approved

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Last modified December 7 05:39 EST 2016. Contains 278841 sequences.