A025411 Numbers that are the sum of 4 distinct positive cubes.

100, 161, 198, 217, 224, 252, 289, 308, 315, 350, 369, 376, 379, 406, 413, 416, 432, 435, 442, 477, 496, 503, 533, 540, 548, 559, 568, 585, 587, 594, 604, 611, 624, 631, 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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

First differs from A025408 at a(80)=1036. - Ray Chandler, Feb 19 2005

Examples

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

Crossrefs

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

Programs

Maple

isA025411:= proc(n)
    local a, x, y, z,wcu ;
    for x from 1 do
        if 4*x^3 > n then
            return false;
            end if;
        for y from x+1 do
            if x^3+3*y^3 > n then
                break;
            end if;
            for z from y+1 do
                if x^3+y^3+2*z^3 > n then
                    break;
                end if;
                wcu := n-x^3-y^3-z^3 ;
                if wcu > z^3 and isA000578(wcu) then
                    return true ;
                end if;
            end do
        end do:
    end do:
end proc:
for n from 1 to 1100 do
    if isA025411(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jun 15 2018

Mathematica

smax = 1036;
imax = smax^(1/3) // Ceiling;
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 *)

Extensions

More terms from Ray Chandler, Feb 19 2005