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%I #11 Aug 12 2015 02:00:55
%S 0,3,23,69,155,293,508,799,1205,1732,2395,3218,4216,5412,6821,8502,
%T 10416,12629,15137,17996,21173,24768,28755,33164,38020,43341,49162,
%U 55550,62485,70004,78123,86862,96254,106392,117211,128754,141147,154276
%N a(n) = number of solutions to the Diophantine equation x+y^2+z^3=n^4 with positive x,y,z all distinct.
%e 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}.
%e 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}.
%p 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
%Y Cf. A121876 = Diophantine equation x+y^2+z^3=n^4.
%K nonn
%O 1,2
%A _Zak Seidov_, Sep 09 2006
%E More terms from _R. J. Mathar_, Jan 13 2007
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