A003381 - OEIS

%I #25 May 02 2023 11:11:46

%S 3,258,513,768,6563,6818,7073,13123,13378,19683,65538,65793,66048,

%T 72098,72353,78658,131073,131328,137633,196608,390627,390882,391137,

%U 397187,397442,403747,456162,456417,462722,521697,781251,781506,787811,846786

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

%H R. J. Mathar, <a href="/A003381/b003381.txt">Table of n, a(n) for n = 1..8000</a> (replacing an earlier b-file that missed terms).

%p A003381 := proc(nmax::integer)

%p     local xyzmax, ins, x,x8,y,y8,z,z8 ;

%p         xyzmax := ceil(root[8](nmax/3)) ;

%p         a := {} ;

%p         for x from 1 to xyzmax do

%p                 x8 := x^8 ;

%p                 if 3*x8 > nmax then

%p                         break;

%p                 end if;

%p                 for y from x do

%p                         y8 := y^8 ;

%p                         if x8+2*y8 > nmax then

%p                                 break;

%p                         end if;

%p                         for z from y do

%p                                 z8 := z^8 ;

%p                                 if x8+y8+z8 > nmax then

%p                                         break;

%p                                 end if;

%p                                 if x8+y8+z8 <= nmax then

%p                                         a := a  union {x8+y8+z8} ;

%p                                 end if;

%p                         end do:

%p                 end do:

%p         end do:

%p         sort(convert(a,list)) ;

%p end proc:

%p nmax := 6755626171875 ;

%p L:= A003381(nmax) ;

%p LISTTOBFILE(L,"b003381.txt",1) ; # _R. J. Mathar_, Aug 01 2020

%t kmax = 4*10^12;

%t m = kmax^(1/8) // Ceiling;

%t 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 *)

%Y Cf. A001016 (8th powers).

%K nonn

%O 1,1

%A _N. J. A. Sloane_