OFFSET
1,1
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 6751 terms from R. J. Mathar, replacing an earlier file that missed terms)
MAPLE
A003385 := proc(nmax::integer)
local a, x, x8, y, y8, z, z8, u, u8, v, v8, w, w8, t, t8 ;
a := {} ;
for x from 1 do
x8 := x^8 ;
if 7*x8 > nmax then
break;
end if;
for y from x do
y8 := y^8 ;
if x8+6*y8 > nmax then
break;
end if;
for z from y do
z8 := z^8 ;
if x8+y8+5*z8 > nmax then
break;
end if;
for u from z do
u8 := u^8 ;
if x8+y8+z8+4*u8 > nmax then
break;
end if;
for v from u do
v8 := v^8 ;
if x8+y8+z8+u8+3*v8 > nmax then
break;
end if;
for w from v do
w8 := w^8 ;
if x8+y8+z8+u8+v8+2*w8 > nmax then
break;
end if;
for t from w do
t8 := t^8 ;
if x8+y8+z8+u8+v8+w8+t8 > nmax then
break;
end if;
if x8+y8+z8+u8+v8+w8+t8 <= nmax then
a := a union {x8+y8+z8+u8+v8+w8+t8} ;
end if;
end do:
end do:
end do:
end do:
end do:
end do:
end do:
sort(convert(a, list)) ;
end proc:
nmax := 117440512 ;
L:= A003385(nmax) ;
LISTTOBFILE(L, "b003385.txt", 1) ; # R. J. Mathar, Aug 01 2020
MATHEMATICA
M = 217168099;
m = M^(1/8) // Ceiling;
Table[s = a^8+b^8+c^8+d^8+e^8+f^8+g^8; If[s>M, Nothing, s], {a, m}, {b, m}, {c, m}, {d, m}, {e, m}, {f, m}, {g, m}] // Flatten // Union (* Jean-François Alcover, Dec 01 2020 *)
PROG
(PARI) \\ also works for nmax=117440512 producing 6751 terms
nmax=67000; v=vectorsmall(nmax); L=ceil(#v^(1/8)); for(k1=1, L, for(k2=k1, L, for(k3=k2, L, for(k4=k3, L, for(k5=k4, L, for(k6=k5, L, for(k7=k6, L, my(s=k1^8+k2^8+k3^8+k4^8+k5^8+k6^8+k7^8); if(s<=#v, v[s]++)))))))); for(k=1, #v, if(v[k], print1(k, ", "))) \\ Hugo Pfoertner, Aug 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,easy
AUTHOR
EXTENSIONS
Incorrect program removed by David A. Corneth, Aug 04 2020
STATUS
approved