A003387 Numbers that are the sum of 9 nonzero 8th powers.

9, 264, 519, 774, 1029, 1284, 1539, 1794, 2049, 2304, 6569, 6824, 7079, 7334, 7589, 7844, 8099, 8354, 8609, 13129, 13384, 13639, 13894, 14149, 14404, 14659, 14914, 19689, 19944, 20199, 20454, 20709, 20964, 21219, 26249, 26504, 26759, 27014, 27269

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 3854 terms from R. J. Mathar, replacing an earlier file that was missing terms)

Example

From David A. Corneth, Aug 01 2020: (Start)
5820102 is in the sequence as 5820102 = 1^8 + 1^8 + 1^8 + 1^8 + 5^8 + 5^8 + 6^8 + 6^8 + 6^8.
9960580 is in the sequence as 9960580 = 5^8 + 5^8 + 5^8 + 5^8 + 6^8 + 6^8 + 6^8 + 6^8 + 6^8.
11260068 is in the sequence as 11260068 = 1^8 + 1^8 + 2^8 + 4^8 + 5^8 + 6^8 + 6^8 + 6^8 + 7^8. (End)

Maple

A003387 := proc(nmax::integer)
    local a, x, x8, y, y8, z, z8, u, u8, v, v8, w, w8, t, t8, s, s8, r, r8 ;
    a := {} ;
    for x from 1 do
        x8 := x^8 ;
        if 9*x8 > nmax then
            break;
        end if;
        for y from x do
            y8 := y^8 ;
            if x8+8*y8 > nmax then
                break;
            end if;
            for z from y do
                z8 := z^8 ;
                if x8+y8+7*z8 > nmax then
                    break;
                end if;
                for u from z do
                    u8 := u^8 ;
                    if x8+y8+z8+6*u8 > nmax then
                        break;
                    end if;
                    for v from u do
                        v8 := v^8 ;
                        if x8+y8+z8+u8+5*v8 > nmax then
                            break;
                        end if;
                        for w from v do
                            w8 := w^8 ;
                            if x8+y8+z8+u8+v8+4*w8 > nmax then
                                break;
                            end if;
                            for t from w do
                                t8 := t^8 ;
                                if x8+y8+z8+u8+v8+w8+3*t8 > nmax then
                                    break;
                                end if;
                                for s from t do
                                    s8 := s^8 ;
                                    if x8+y8+z8+u8+v8+w8+t8+2*s8 > nmax then
                                        break;
                                    end if;
                                    for r from s do
                                        r8 := r^8 ;
                                        if x8+y8+z8+u8+v8+w8+t8+s8+r8 > nmax then
                                            break ;
                                        end if;
                                        if x8+y8+z8+u8+v8+w8+t8+s8+r8 <= nmax then
                                            a := a  union {x8+y8+z8+u8+v8+w8+t8+s8+r8} ;
                                        end if;
                                    end do:
                                end do:
                            end do:
                        end do:
                    end do:
                end do:
            end do:
        end do:
    end do:
    sort(convert(a, list)) ;
end proc:
nmax := 15116544 ;
L:= A003387(nmax) ;
LISTTOBFILE(L, "b003387.txt", 1) ; # R. J. Mathar, Aug 01 2020

Mathematica

M = 45711012; m = M^(1/8) // Ceiling; Reap[
For[a = 1, a <= m, a++, For[b = a, b <= m, b++, For[c = b, c <= m, c++,
For[d = c, d <= m, d++, For[e = d, e <= m, e++, For[f = e, f <= m, f++,
For[g = f, g <= m, g++, For[h = g, h <= m, h++, For[i = h, i <= m, i++,
s = a^8 + b^8 + c^8 + d^8 + e^8 + f^8 + g^8 + h^8 + i^8;
If[s <= M, Sow[s]]]]]]]]]]]][[2, 1]] // Union (* Jean-François Alcover, Dec 01 2020 *)

Crossrefs

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: A173985 A280178 A189643 * A177393 A081059 A202884

Adjacent sequences: A003384 A003385 A003386 * A003388 A003389 A003390

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved