A003387 Numbers that are the sum of 9 nonzero 8th powers.
9, 264, 519, 774, 1029, 1284, 1539, 1794, 2049, 2304, 6569, 6824, 7079, 7334, 7589, 7844, 8099, 8354, 8609, 13129, 13384, 13639, 13894, 14149, 14404, 14659, 14914, 19689, 19944, 20199, 20454, 20709, 20964, 21219, 26249, 26504, 26759, 27014, 27269
Offset: 1
Examples
From _David A. Corneth_, Aug 01 2020: (Start) 5820102 is in the sequence as 5820102 = 1^8 + 1^8 + 1^8 + 1^8 + 5^8 + 5^8 + 6^8 + 6^8 + 6^8. 9960580 is in the sequence as 9960580 = 5^8 + 5^8 + 5^8 + 5^8 + 6^8 + 6^8 + 6^8 + 6^8 + 6^8. 11260068 is in the sequence as 11260068 = 1^8 + 1^8 + 2^8 + 4^8 + 5^8 + 6^8 + 6^8 + 6^8 + 7^8. (End)
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3854 terms from R. J. Mathar, replacing an earlier file that was missing terms)
Crossrefs
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
A003387 := proc(nmax::integer) local a, x,x8,y,y8,z,z8,u,u8,v,v8,w,w8,t,t8,s,s8,r,r8 ; a := {} ; for x from 1 do x8 := x^8 ; if 9*x8 > nmax then break; end if; for y from x do y8 := y^8 ; if x8+8*y8 > nmax then break; end if; for z from y do z8 := z^8 ; if x8+y8+7*z8 > nmax then break; end if; for u from z do u8 := u^8 ; if x8+y8+z8+6*u8 > nmax then break; end if; for v from u do v8 := v^8 ; if x8+y8+z8+u8+5*v8 > nmax then break; end if; for w from v do w8 := w^8 ; if x8+y8+z8+u8+v8+4*w8 > nmax then break; end if; for t from w do t8 := t^8 ; if x8+y8+z8+u8+v8+w8+3*t8 > nmax then break; end if; for s from t do s8 := s^8 ; if x8+y8+z8+u8+v8+w8+t8+2*s8 > nmax then break; end if; for r from s do r8 := r^8 ; if x8+y8+z8+u8+v8+w8+t8+s8+r8 > nmax then break ; end if; if x8+y8+z8+u8+v8+w8+t8+s8+r8 <= nmax then a := a union {x8+y8+z8+u8+v8+w8+t8+s8+r8} ; end if; end do: end do: end do: end do: end do: end do: end do: end do: end do: sort(convert(a,list)) ; end proc: nmax := 15116544 ; L:= A003387(nmax) ; LISTTOBFILE(L,"b003387.txt",1) ; # R. J. Mathar, Aug 01 2020
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Mathematica
M = 45711012; m = M^(1/8) // Ceiling; Reap[ For[a = 1, a <= m, a++, For[b = a, b <= m, b++, For[c = b, c <= m, c++, For[d = c, d <= m, d++, For[e = d, e <= m, e++, For[f = e, f <= m, f++, For[g = f, g <= m, g++, For[h = g, h <= m, h++, For[i = h, i <= m, i++, s = a^8 + b^8 + c^8 + d^8 + e^8 + f^8 + g^8 + h^8 + i^8; If[s <= M, Sow[s]]]]]]]]]]]][[2, 1]] // Union (* Jean-François Alcover, Dec 01 2020 *)
Extensions
Incorrect program removed by David A. Corneth, Aug 01 2020
Comments