A003385 Numbers that are the sum of 7 nonzero 8th powers.
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
Offset: 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)
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).
Programs
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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
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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 *) -
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
Extensions
Incorrect program removed by David A. Corneth, Aug 04 2020