Numbers that are not the sum of 8 nonnegative fifth powers.
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89
1
There are 108635543 such numbers; these are the first 1000.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Waring’s problem
(Mma) nn = 5; lim = nn^5; t8 = Table[0, {lim}]; Do[num = i^5 + j^5 + k^5 + l^5 + m^5 + n^5 + o^5 + p^5; If[0 < num <= lim, t8[[num]]++], {i, 0, nn}, {j, i, nn}, {k, j, nn}, {l, k, nn}, {m, l, nn}, {n, m, nn}, {o, n, nn}, {p, o, nn}]; Take[Flatten[Position[t8, 0]], 1000]
nonn,fini
T. D. Noe, Jun 14 2017