A121876 a(n) = number of solutions to the Diophantine equation x+y^2+z^3=n^4 with positive x,y,z.

0, 5, 27, 75, 163, 303, 521, 815, 1223, 1753, 2419, 3245, 4246, 5445, 6857, 8541, 10459, 12675, 15187, 18049, 21230, 24829, 28820, 33232, 38092, 43417, 49243, 55634, 62573, 70096, 78220, 86963, 96359, 106501, 117325, 128873, 141269

Offset

1,2

Links

R. J. Mathar, Table of n, a(n) for n = 1..214

Example

a(2)=5 because there are five solutions to equation x+y^2+z^3=2^4 with {x,y,z}={4,2,2},{6,3,1},{7,1,2},{11,2,1},{14,1,1};
a(3)=27 because there are 27 solutions to equation x+y^2+z^3=3^4 with
{x, y, z}={1, 4, 4}, {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}, {45, 3, 3}, {48, 5, 2}, {50, 2, 3}, {53, 1, 3}, {55, 5, 1}, {57, 4, 2}, {64, 3, 2}, {64, 4, 1}, {69, 2, 2}, {71, 3, 1}, {72, 1, 2}, {76, 2, 1}, {79, 1, 1}

Prog

(C++) #include <iostream> #include <math.h> #include <limits.h> using namespace std ; int main(int argc, char *argv[]) { const int nmax=sqrt(sqrt(INT_MAX)) ; for(int n=1; n < nmax ; n++) { int a=0 ; const int n4=n*n*n*n ; for(int z=1; ; z++) { const int z3=z*z*z ; if( z3 >= n4) break ; for(int y=1; y*y+z3 < n4 ; y++) { if ( n4-z3-y*y > 0) a++ ; } } cout << n << " " << a << endl ; } return 0 ; } - R. J. Mathar, Sep 12 2006

Crossrefs

Sequence in context: A136917 A181890 A048712 * A137116 A137117 A064675

Adjacent sequences: A121873 A121874 A121875 * A121877 A121878 A121879

Keyword

nonn

Author

Zak Seidov, Sep 09 2006

Extensions

More terms from R. J. Mathar and Max Alekseyev, Sep 10 2006

Status

approved