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

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)
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)
		

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)

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).

Programs

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 *)

Extensions

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