A003381 Numbers that are the sum of 3 nonzero 8th powers.

3, 258, 513, 768, 6563, 6818, 7073, 13123, 13378, 19683, 65538, 65793, 66048, 72098, 72353, 78658, 131073, 131328, 137633, 196608, 390627, 390882, 391137, 397187, 397442, 403747, 456162, 456417, 462722, 521697, 781251, 781506, 787811, 846786

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..8000 (replacing an earlier b-file that missed terms).

Crossrefs

Cf. A001016 (8th powers).

Programs

Maple

A003381 := proc(nmax::integer)
    local xyzmax, ins, x,x8,y,y8,z,z8 ;
        xyzmax := ceil(root[8](nmax/3)) ;
        a := {} ;
        for x from 1 to xyzmax do
                x8 := x^8 ;
                if 3*x8 > nmax then
                        break;
                end if;
                for y from x do
                        y8 := y^8 ;
                        if x8+2*y8 > nmax then
                                break;
                        end if;
                        for z from y do
                                z8 := z^8 ;
                                if x8+y8+z8 > nmax then
                                        break;
                                end if;
                                if x8+y8+z8 <= nmax then
                                        a := a  union {x8+y8+z8} ;
                                end if;
                        end do:
                end do:
        end do:
        sort(convert(a,list)) ;
end proc:
nmax := 6755626171875 ;
L:= A003381(nmax) ;
LISTTOBFILE(L,"b003381.txt",1) ; # R. J. Mathar, Aug 01 2020

Mathematica

kmax = 4*10^12;
m = kmax^(1/8) // Ceiling;
Table[k = x^8 + y^8 + z^8; If[k <= kmax, k, Nothing], {x, 1, m}, {y, x, m}, {z, y, m}] // Flatten // Union (* Jean-François Alcover, May 02 2023 *)