A003382 Numbers that are the sum of 4 nonzero 8th powers.

4, 259, 514, 769, 1024, 6564, 6819, 7074, 7329, 13124, 13379, 13634, 19684, 19939, 26244, 65539, 65794, 66049, 66304, 72099, 72354, 72609, 78659, 78914, 85219, 131074, 131329, 131584, 137634, 137889, 144194, 196609, 196864, 203169, 262144

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

As the order of addition doesn't matter we can assume terms are in nondecreasing order. - David A. Corneth, Aug 01 2020

Examples

			From _David A. Corneth_, Aug 01 2020: (Start)
1246103043 is in the sequence as 1246103043 = 1^8 + 5^8 + 12^8 + 13^8.
4194358628 is in the sequence as 4194358628 = 3^8 + 13^8 + 13^8 + 15^8.
5148323267 is in the sequence as 5148323267 = 7^8 + 8^8 + 15^8 + 15^8. (End)
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..13540 replacing an earlier file that was missing terms.

Crossrefs

Cf. A001016 (8th powers).

A###### (x, y): Numbers that are the form of x nonzero y-th powers.

Cf. A000404 (2, 2), A000408 (3, 2), A000414 (4, 2), A003072 (3, 3), A003325 (3, 2), A003327 (4, 3), A003328 (5, 3), A003329 (6, 3), A003330 (7, 3), A003331 (8, 3), A003332 (9, 3), A003333 (10, 3), A003334 (11, 3), A003335 (12, 3), A003336 (2, 4), A003337 (3, 4), A003338 (4, 4), A003339 (5, 4), A003340 (6, 4), A003341 (7, 4), A003342 (8, 4), A003343 (9, 4), A003344 (10, 4), A003345 (11, 4), A003346 (12, 4), A003347 (2, 5), A003348 (3, 5), A003349 (4, 5), A003350 (5, 5), A003351 (6, 5), A003352 (7, 5), A003353 (8, 5), A003354 (9, 5), A003355 (10, 5), A003356 (11, 5), A003357 (12, 5), A003358 (2, 6), A003359 (3, 6), A003360 (4, 6), A003361 (5, 6), A003362 (6, 6), A003363 (7, 6), A003364 (8, 6), A003365 (9, 6), A003366 (10, 6), A003367 (11, 6), A003368 (12, 6), A003369 (2, 7), A003370 (3, 7), A003371 (4, 7), A003372 (5, 7), A003373 (6, 7), A003374 (7, 7), A003375 (8, 7), A003376 (9, 7), A003377 (10, 7), A003378 (11, 7), A003379 (12, 7), A003380 (2, 8), A003381 (3, 8), A003382 (4, 8), A003383 (5, 8), A003384 (6, 8), A003385 (7, 8), A003387 (9, 8), A003388 (10, 8), A003389 (11, 8), A003390 (12, 8), A003391 (2, 9), A003392 (3, 9), A003393 (4, 9), A003394 (5, 9), A003395 (6, 9), A003396 (7, 9), A003397 (8, 9), A003398 (9, 9), A003399 (10, 9), A004800 (11, 9), A004801 (12, 9), A004802 (2, 10), A004803 (3, 10), A004804 (4, 10), A004805 (5, 10), A004806 (6, 10), A004807 (7, 10), A004808 (8, 10), A004809 (9, 10), A004810 (10, 10), A004811 (11, 10), A004812 (12, 10), A004813 (2, 11), A004814 (3, 11), A004815 (4, 11), A004816 (5, 11), A004817 (6, 11), A004818 (7, 11), A004819 (8, 11), A004820 (9, 11), A004821 (10, 11), A004822 (11, 11), A004823 (12, 11), A047700 (5, 2).

Programs

Maple

A003382 := proc(nmax::integer)
    local a, x,x8,y,y8,z,z8,u,u8 ;
    a := {} ;
    for x from 1 do
        x8 := x^8 ;
        if 4*x8 > nmax then
            break;
        end if;
        for y from x do
            y8 := y^8 ;
            if x8+3*y8 > nmax then
                break;
            end if;
            for z from y do
                z8 := z^8 ;
                if x8+y8+2*z8 > nmax then
                    break;
                end if;
                for u from z do
                    u8 := u^8 ;
                    if x8+y8+z8+u8 > nmax then
                        break;
                    end if;
                    if x8+y8+z8+u8 <= nmax then
                        a := a  union {x8+y8+z8+u8} ;
                    end if;
                end do:
            end do:
        end do:
    end do:
    sort(convert(a,list)) ;
end proc:
nmax := 102400000000 ;
L:= A003382(nmax) ;
LISTTOBFILE(L,"b003382.txt",1) ; # R. J. Mathar, Aug 01 2020

Mathematica

M = 102400000000;
m = M^(1/8) // Ceiling;
Table[s = a^8+b^8+c^8+d^8; If[s>M, Nothing, s], {a, m}, {b, m}, {c, m}, {d, m}] // Flatten // Union (* Jean-François Alcover, Dec 01 2020 *)

Extensions

Incorrect program removed by David A. Corneth, Aug 01 2020