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
R. J. Mathar, Table of n, a(n) for n = 1..13540 replacing an earlier file that was missing terms.
EXAMPLE
From David A. Corneth, Aug 01 2020: (Start)
1246103043 is in the sequence as 1246103043 = 1^8 + 5^8 + 12^8 + 13^8.
4194358628 is in the sequence as 4194358628 = 3^8 + 13^8 + 13^8 + 15^8.
5148323267 is in the sequence as 5148323267 = 7^8 + 8^8 + 15^8 + 15^8. (End)
MAPLE
A003382 := proc(nmax::integer)
local a, x, x8, y, y8, z, z8, u, u8 ;
a := {} ;
for x from 1 do
x8 := x^8 ;
if 4*x8 > nmax then
break;
end if;
for y from x do
y8 := y^8 ;
if x8+3*y8 > nmax then
break;
end if;
for z from y do
z8 := z^8 ;
if x8+y8+2*z8 > nmax then
break;
end if;
for u from z do
u8 := u^8 ;
if x8+y8+z8+u8 > nmax then
break;
end if;
if x8+y8+z8+u8 <= nmax then
a := a union {x8+y8+z8+u8} ;
end if;
end do:
end do:
end do:
end do:
sort(convert(a, list)) ;
end proc:
nmax := 102400000000 ;
L:= A003382(nmax) ;
LISTTOBFILE(L, "b003382.txt", 1) ; # R. J. Mathar, Aug 01 2020
MATHEMATICA
M = 102400000000;
m = M^(1/8) // Ceiling;
Table[s = a^8+b^8+c^8+d^8; If[s>M, Nothing, s], {a, m}, {b, m}, {c, m}, {d, 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).
KEYWORD
nonn
AUTHOR
EXTENSIONS
Incorrect program removed by David A. Corneth, Aug 01 2020
STATUS
approved