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

1,1

Links

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

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 *)

Crossrefs

Cf. A001016 (8th powers).

Sequence in context: A232545 A177748 A283018 * A219550 A319587 A058451

Adjacent sequences: A003378 A003379 A003380 * A003382 A003383 A003384

Keyword

nonn

Author

N. J. A. Sloane

Status

approved