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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
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
Sequence in context: A103251 A256418 A198387 * A057103 A055669 A335144
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 February 21 10:54 EST 2024. Contains 370233 sequences. (Running on oeis4.)