A003383 Numbers that are the sum of 5 nonzero 8th powers.

5, 260, 515, 770, 1025, 1280, 6565, 6820, 7075, 7330, 7585, 13125, 13380, 13635, 13890, 19685, 19940, 20195, 26245, 26500, 32805, 65540, 65795, 66050, 66305, 66560, 72100, 72355, 72610, 72865, 78660, 78915, 79170, 85220, 85475, 91780, 131075

Offset

1,1

Comments

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

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3302 terms from R. J. Mathar, replacing an earlier b-file that missed terms)

Example

From David A. Corneth, Aug 01 2020: (Start)
100131584 is in the sequence as 100131584 = 2^8 + 2^8 + 4^8 + 4^8 + 10^8.
320123684 is in the sequence as 320123684 = 1^8 + 1^8 + 7^8 + 10^8 + 11^8.
750105634 is in the sequence as 750105634 = 2^8 + 7^8 + 10^8 + 11^8 + 12^8. (End)

Maple

A003383 := proc(nmax::integer)
    local a, x, x8, y, y8, z, z8, u, u8, v, v8 ;
    a := {} ;
    for x from 1 do
        x8 := x^8 ;
        if 5*x8 > nmax then
            break;
        end if;
        for y from x do
            y8 := y^8 ;
            if x8+4*y8 > nmax then
                break;
            end if;
            for z from y do
                z8 := z^8 ;
                if x8+y8+3*z8 > nmax then
                    break;
                end if;
                for u from z do
                    u8 := u^8 ;
                    if x8+y8+z8+2*u8 > nmax then
                        break;
                    end if;
                    for v from u do
                        v8 := v^8 ;
                        if x8+y8+z8+u8+v8 > nmax then
                            break;
                        end if;
                        if x8+y8+z8+u8+v8 <= nmax then
                            a := a  union {x8+y8+z8+u8+v8} ;
                        end if;
                    end do:
                end do:
            end do:
        end do:
    end do:
    sort(convert(a, list)) ;
end proc:
nmax := 500000000 ; ;
L:= A003383(nmax) ;
LISTTOBFILE(L, "b003383.txt", 1) ; # R. J. Mathar, Aug 01 2020

Mathematica

M = 3784086305;
m = M^(1/8) // Ceiling;
Table[s = a^8+b^8+c^8+d^8+e^8; If[s>M, Nothing, s], {a, m}, {b, m}, {c, m}, {d, m}, {e, m}] // Flatten // Union (* Jean-François Alcover, Dec 01 2020 *)

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).

Sequence in context: A139000 A061959 A002554 * A195575 A195553 A142254

Adjacent sequences: A003380 A003381 A003382 * A003384 A003385 A003386

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved