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A004893 Numbers that are the sum of at most 9 positive 9th powers.

%I A004893 #18 May 20 2022 07:54:19
%S A004893 0,1,2,3,4,5,6,7,8,9,512,513,514,515,516,517,518,519,520,1024,1025,
%T A004893 1026,1027,1028,1029,1030,1031,1536,1537,1538,1539,1540,1541,1542,
%U A004893 2048,2049,2050,2051,2052,2053,2560,2561,2562,2563,2564,3072,3073,3074,3075,3584
%N A004893 Numbers that are the sum of at most 9 positive 9th powers.
%H A004893 Alois P. Heinz, <a href="/A004893/b004893.txt">Table of n, a(n) for n = 1..10000</a>
%p A004893 b:= proc(n, i, t) option remember; n=0 or i>0 and t>0
%p A004893       and (b(n, i-1, t) or i^9<=n and b(n-i^9, i, t-1))
%p A004893     end:
%p A004893 a:= proc(n) option remember; local k;
%p A004893       for k from 1+ `if`(n=1, -1, a(n-1))
%p A004893       while not b(k, iroot(k, 9), 9) do od; k
%p A004893     end:
%p A004893 seq(a(n), n=1..60);  # _Alois P. Heinz_, Sep 16 2016
%t A004893 b[n_, k_, i_, t_] := b[n, k, i, t] = n == 0 || i > 0 && t > 0 && (b[n, k, i - 1, t] || i^k <= n && b[n - i^k, k, i, t - 1]);
%t A004893 A[n_, k_] := A[n, k] = Module[{m}, For[m = 1 + If[n == 1, -1, A[n - 1, k]], !b[m, k, m^(1/k) // Floor, k], m++]; m];
%t A004893 a[n_] := A[n, 9];
%t A004893 Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, May 20 2022, after _Alois P. Heinz_ in A336820 *)
%Y A004893 Column k=9 of A336820.
%K A004893 nonn
%O A004893 1,3
%A A004893 _N. J. A. Sloane_
%E A004893 More terms from _Alois P. Heinz_, Sep 16 2016