|
|
A003382
|
|
Numbers that are the sum of 4 nonzero 8th powers.
|
|
30
|
|
|
4, 259, 514, 769, 1024, 6564, 6819, 7074, 7329, 13124, 13379, 13634, 19684, 19939, 26244, 65539, 65794, 66049, 66304, 72099, 72354, 72609, 78659, 78914, 85219, 131074, 131329, 131584, 137634, 137889, 144194, 196609, 196864, 203169, 262144
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
EXAMPLE
|
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
|
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 ;
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
|
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
|
|
|
STATUS
|
approved
|
|
|
|