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).
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Incorrect program removed by David A. Corneth, Aug 01 2020
STATUS
approved