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

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 512, 513, 514, 515, 516, 517, 518, 519, 520, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 2048, 2049, 2050, 2051, 2052, 2053, 2560, 2561, 2562, 2563, 2564, 3072, 3073, 3074, 3075, 3584

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Column k=9 of A336820.

Programs

Maple

b:= proc(n, i, t) option remember; n=0 or i>0 and t>0
      and (b(n, i-1, t) or i^9<=n and b(n-i^9, i, t-1))
    end:
a:= proc(n) option remember; local k;
      for k from 1+ `if`(n=1, -1, a(n-1))
      while not b(k, iroot(k, 9), 9) do od; k
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Sep 16 2016

Mathematica

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]);
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];
a[n_] := A[n, 9];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, May 20 2022, after Alois P. Heinz in A336820 *)

Extensions

More terms from Alois P. Heinz, Sep 16 2016