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A003385
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Numbers that are the sum of 7 nonzero 8th powers.
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30
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7, 262, 517, 772, 1027, 1282, 1537, 1792, 6567, 6822, 7077, 7332, 7587, 7842, 8097, 13127, 13382, 13637, 13892, 14147, 14402, 19687, 19942, 20197, 20452, 20707, 26247, 26502, 26757, 27012, 32807, 33062, 33317, 39367, 39622, 45927, 65542, 65797, 66052
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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MAPLE
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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 ;
LISTTOBFILE(L, "b003385.txt", 1) ; # R. J. Mathar, Aug 01 2020
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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