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%I #42 Apr 27 2024 20:03:03
%S 2,257,512,6562,6817,13122,65537,65792,72097,131072,390626,390881,
%T 397186,456161,781250,1679617,1679872,1686177,1745152,2070241,3359232,
%U 5764802,5765057,5771362,5830337,6155426,7444417,11529602,16777217,16777472,16783777,16842752
%N Numbers that are the sum of 2 nonzero 8th powers.
%H David A. Corneth, <a href="/A003380/b003380.txt">Table of n, a(n) for n = 1..10000</a> (first 5833 terms from R. J. Mathar, replacing an earlier b-file that was missing terms)
%e From _David A. Corneth_, Aug 01 2020: (Start)
%e 274893519322337 is in the sequence as 274893519322337 = 58^8 + 59^8.
%e 357707312890625 is in the sequence as 357707312890625 = 50^8 + 65^8.
%e 2590188068194497 is in the sequence as 2590188068194497 = 57^8 + 84^8. (End)
%p A003380 := proc(nmax::integer)
%p local a, x,x8,y,y8 ;
%p a := {} ;
%p for x from 1 do
%p x8 := x^8 ;
%p if 2*x8 > nmax then
%p break;
%p end if;
%p for y from x do
%p y8 := y^8 ;
%p if x8+y8 > nmax then
%p break;
%p end if;
%p if x8+y8 <= nmax then
%p a := a union {x8+y8} ;
%p end if;
%p end do:
%p end do:
%p sort(convert(a,list)) ;
%p end proc:
%p nmax := 20000000000000000 ;
%p L:= A003380(nmax) ;
%p LISTTOBFILE(L,"b003380.txt",1) ; # _R. J. Mathar_, Aug 01 2020
%t Total/@Tuples[Range[8]^8,2]//Union (* _Harvey P. Dale_, Apr 04 2017 *)
%o (PARI) list(lim)=my(v=List(), x8); for(x=1, sqrtnint(lim\=1, 8), x8=x^8; for(y=1, min(sqrtnint(lim-x8, 8), x), listput(v, x8+y^8))); Set(v) \\ _Charles R Greathouse IV_, Aug 22 2017
%Y Subsequence of A004875.
%Y Cf. A155468 (2 distinct 8th).
%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_
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