%I #19 Jun 26 2023 05:32:54

%S 100,161,198,217,224,252,289,308,315,350,369,376,379,406,413,416,432,

%T 435,442,477,496,503,533,540,548,559,568,585,587,594,604,611,624,631,

%U 646,650,665,672,685,692,702,709,711,728,737,748,756,763,765,793,800,802,819,821,828,854,861,863,864,880,882,883,889,890,917,919,920,926,927,945,946,954,973,980,981,988,1007,1010,1017,1036

%N Numbers that are the sum of 4 distinct positive cubes.

%C First differs from A025408 at a(80)=1036. - _Ray Chandler_, Feb 19 2005

%e a(80) = 1036 = 1+8+27+1000 = 27+64+216+729.

%p isA025411:= proc(n)

%p local a, x, y, z,wcu ;

%p for x from 1 do

%p if 4*x^3 > n then

%p return false;

%p end if;

%p for y from x+1 do

%p if x^3+3*y^3 > n then

%p break;

%p end if;

%p for z from y+1 do

%p if x^3+y^3+2*z^3 > n then

%p break;

%p end if;

%p wcu := n-x^3-y^3-z^3 ;

%p if wcu > z^3 and isA000578(wcu) then

%p return true ;

%p end if;

%p end do

%p end do:

%p end do:

%p end proc:

%p for n from 1 to 1100 do

%p if isA025411(n) then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Jun 15 2018

%t smax = 1036;

%t imax = smax^(1/3) // Ceiling;

%t Table[If[Less[i, j, k, l] && (s = i^3 + j^3 + k^3 + l^3) <= smax, s, Nothing], {i, 1, imax}, {j, i+1, imax}, {k, j+1, imax}, {l, k+1, imax}] // Flatten // Union (* _Jean-François Alcover_, Jun 26 2023 *)

%Y Cf. A025408, A025409, A025410, A025412, A025413.

%K nonn

%O 1,1

%A _David W. Wilson_

%E More terms from _Ray Chandler_, Feb 19 2005