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

%I A003381 #25 May 02 2023 11:11:46
%S A003381 3,258,513,768,6563,6818,7073,13123,13378,19683,65538,65793,66048,
%T A003381 72098,72353,78658,131073,131328,137633,196608,390627,390882,391137,
%U A003381 397187,397442,403747,456162,456417,462722,521697,781251,781506,787811,846786
%N A003381 Numbers that are the sum of 3 nonzero 8th powers.
%H A003381 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 A003381 := proc(nmax::integer)
%p A003381     local xyzmax, ins, x,x8,y,y8,z,z8 ;
%p A003381         xyzmax := ceil(root[8](nmax/3)) ;
%p A003381         a := {} ;
%p A003381         for x from 1 to xyzmax do
%p A003381                 x8 := x^8 ;
%p A003381                 if 3*x8 > nmax then
%p A003381                         break;
%p A003381                 end if;
%p A003381                 for y from x do
%p A003381                         y8 := y^8 ;
%p A003381                         if x8+2*y8 > nmax then
%p A003381                                 break;
%p A003381                         end if;
%p A003381                         for z from y do
%p A003381                                 z8 := z^8 ;
%p A003381                                 if x8+y8+z8 > nmax then
%p A003381                                         break;
%p A003381                                 end if;
%p A003381                                 if x8+y8+z8 <= nmax then
%p A003381                                         a := a  union {x8+y8+z8} ;
%p A003381                                 end if;
%p A003381                         end do:
%p A003381                 end do:
%p A003381         end do:
%p A003381         sort(convert(a,list)) ;
%p A003381 end proc:
%p A003381 nmax := 6755626171875 ;
%p A003381 L:= A003381(nmax) ;
%p A003381 LISTTOBFILE(L,"b003381.txt",1) ; # _R. J. Mathar_, Aug 01 2020
%t A003381 kmax = 4*10^12;
%t A003381 m = kmax^(1/8) // Ceiling;
%t A003381 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 A003381 Cf. A001016 (8th powers).
%K A003381 nonn
%O A003381 1,1
%A A003381 _N. J. A. Sloane_