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%I #30 Oct 29 2023 21:49:07
%S 5,260,515,770,1025,1280,6565,6820,7075,7330,7585,13125,13380,13635,
%T 13890,19685,19940,20195,26245,26500,32805,65540,65795,66050,66305,
%U 66560,72100,72355,72610,72865,78660,78915,79170,85220,85475,91780,131075
%N Numbers that are the sum of 5 nonzero 8th powers.
%C As the order of addition doesn't matter we can assume terms are in nondecreasing order. - _David A. Corneth_, Aug 01 2020
%H David A. Corneth, <a href="/A003383/b003383.txt">Table of n, a(n) for n = 1..10000</a> (first 3302 terms from R. J. Mathar, replacing an earlier b-file that missed terms)
%e From _David A. Corneth_, Aug 01 2020: (Start)
%e 100131584 is in the sequence as 100131584 = 2^8 + 2^8 + 4^8 + 4^8 + 10^8.
%e 320123684 is in the sequence as 320123684 = 1^8 + 1^8 + 7^8 + 10^8 + 11^8.
%e 750105634 is in the sequence as 750105634 = 2^8 + 7^8 + 10^8 + 11^8 + 12^8. (End)
%p A003383 := proc(nmax::integer)
%p local a, x,x8,y,y8,z,z8,u,u8,v,v8 ;
%p a := {} ;
%p for x from 1 do
%p x8 := x^8 ;
%p if 5*x8 > nmax then
%p break;
%p end if;
%p for y from x do
%p y8 := y^8 ;
%p if x8+4*y8 > nmax then
%p break;
%p end if;
%p for z from y do
%p z8 := z^8 ;
%p if x8+y8+3*z8 > nmax then
%p break;
%p end if;
%p for u from z do
%p u8 := u^8 ;
%p if x8+y8+z8+2*u8 > nmax then
%p break;
%p end if;
%p for v from u do
%p v8 := v^8 ;
%p if x8+y8+z8+u8+v8 > nmax then
%p break;
%p end if;
%p if x8+y8+z8+u8+v8 <= nmax then
%p a := a union {x8+y8+z8+u8+v8} ;
%p end if;
%p end do:
%p end do:
%p end do:
%p end do:
%p end do:
%p sort(convert(a,list)) ;
%p end proc:
%p nmax := 500000000 ; ;
%p L:= A003383(nmax) ;
%p LISTTOBFILE(L,"b003383.txt",1) ; # _R. J. Mathar_, Aug 01 2020
%t M = 3784086305;
%t m = M^(1/8) // Ceiling;
%t 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 *)
%Y Cf. A001016 (8th powers).
%Y A###### (x, y): Numbers that are the form of x nonzero y-th powers.
%Y 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).
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_