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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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)
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)
		

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)

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

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 *)