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A003383
Numbers that are the sum of 5 nonzero 8th powers.
30
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
1,1
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 3302 terms from R. J. Mathar, replacing an earlier b-file that missed terms)
EXAMPLE
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)
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 *)
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).
Sequence in context: A139000 A061959 A002554 * A195575 A195553 A142254
KEYWORD
nonn,easy
STATUS
approved