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%I #34 Oct 29 2023 21:49:28
%S 7,262,517,772,1027,1282,1537,1792,6567,6822,7077,7332,7587,7842,8097,
%T 13127,13382,13637,13892,14147,14402,19687,19942,20197,20452,20707,
%U 26247,26502,26757,27012,32807,33062,33317,39367,39622,45927,65542,65797,66052
%N Numbers that are the sum of 7 nonzero 8th powers.
%H David A. Corneth, <a href="/A003385/b003385.txt">Table of n, a(n) for n = 1..10000</a> (first 6751 terms from R. J. Mathar, replacing an earlier file that missed terms)
%p A003385 := proc(nmax::integer)
%p local a, x,x8,y,y8,z,z8,u,u8,v,v8,w,w8,t,t8 ;
%p a := {} ;
%p for x from 1 do
%p x8 := x^8 ;
%p if 7*x8 > nmax then
%p break;
%p end if;
%p for y from x do
%p y8 := y^8 ;
%p if x8+6*y8 > nmax then
%p break;
%p end if;
%p for z from y do
%p z8 := z^8 ;
%p if x8+y8+5*z8 > nmax then
%p break;
%p end if;
%p for u from z do
%p u8 := u^8 ;
%p if x8+y8+z8+4*u8 > nmax then
%p break;
%p end if;
%p for v from u do
%p v8 := v^8 ;
%p if x8+y8+z8+u8+3*v8 > nmax then
%p break;
%p end if;
%p for w from v do
%p w8 := w^8 ;
%p if x8+y8+z8+u8+v8+2*w8 > nmax then
%p break;
%p end if;
%p for t from w do
%p t8 := t^8 ;
%p if x8+y8+z8+u8+v8+w8+t8 > nmax then
%p break;
%p end if;
%p if x8+y8+z8+u8+v8+w8+t8 <= nmax then
%p a := a union {x8+y8+z8+u8+v8+w8+t8} ;
%p end if;
%p end do:
%p end do:
%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 := 117440512 ;
%p L:= A003385(nmax) ;
%p LISTTOBFILE(L,"b003385.txt",1) ; # _R. J. Mathar_, Aug 01 2020
%t M = 217168099;
%t m = M^(1/8) // Ceiling;
%t 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 *)
%o (PARI) \\ also works for nmax=117440512 producing 6751 terms
%o 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
%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_
%E Incorrect program removed by _David A. Corneth_, Aug 04 2020
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