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A121984 a(n) = number of solutions to the Diophantine equation x+y^2+z^3=n^4 with positive x,y,z all distinct. 1
0, 3, 23, 69, 155, 293, 508, 799, 1205, 1732, 2395, 3218, 4216, 5412, 6821, 8502, 10416, 12629, 15137, 17996, 21173, 24768, 28755, 33164, 38020, 43341, 49162, 55550, 62485, 70004, 78123, 86862, 96254, 106392, 117211, 128754, 141147, 154276 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

a(2)=3 because there are 3 solutions to equation x+y^2+z^3=2^4 with all distinct {x,y,z}={6,3,1},{7,1,2},{11,2,1}.

a(3)=23 because there are 23 solutions to equation x+y^2+z^3=3^4 with all distinct {x, y, z}={5, 7, 3}, {8, 3, 4}, {9, 8, 2}, {13, 2, 4}, {16, 1, 4}, {16, 8, 1}, {18, 6, 3}, {24, 7, 2}, {29, 5, 3}, {31, 7, 1}, {37, 6, 2}, {38, 4, 3}, {44, 6, 1}, {48, 5, 2}, {50, 2, 3}, {53, 1, 3}, {55, 5, 1}, {57, 4, 2}, {64, 3, 2}, {64, 4, 1}, {71, 3, 1}, {72, 1, 2}, {76, 2, 1}.

MAPLE

A121984 := proc(n) local res, x, y, z, n4 ; res := 0 ; n4 := n^4 ; for y from 1 to n^2 do for z from 1 to n^2 do x := n4-y^2-z^3 ; if x > 0 and x <> y and x <> z and y<> z then res := res+1 ; fi ; if x < 0 then break ; fi ; od ; od ; RETURN(res) ; end ; for n from 1 to 60 do printf("%d, ", A121984(n)) ; od ; # R. J. Mathar, Jan 13 2007

CROSSREFS

Cf. A121876 = Diophantine equation x+y^2+z^3=n^4.

Sequence in context: A183332 A196325 A003531 * A107177 A096207 A163210

Adjacent sequences:  A121981 A121982 A121983 * A121985 A121986 A121987

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 09 2006

EXTENSIONS

More terms from R. J. Mathar, Jan 13 2007

STATUS

approved

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Last modified January 21 17:07 EST 2019. Contains 319350 sequences. (Running on oeis4.)