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A004869 Numbers that are the sum of at most 7 positive 7th powers.

%I A004869 #22 May 20 2022 04:59:43
%S A004869 0,1,2,3,4,5,6,7,128,129,130,131,132,133,134,256,257,258,259,260,261,
%T A004869 384,385,386,387,388,512,513,514,515,640,641,642,768,769,896,2187,
%U A004869 2188,2189,2190,2191,2192,2193,2315,2316,2317,2318,2319,2320,2443,2444,2445
%N A004869 Numbers that are the sum of at most 7 positive 7th powers.
%H A004869 Alois P. Heinz, <a href="/A004869/b004869.txt">Table of n, a(n) for n = 1..15469</a>
%p A004869 b:= proc(n, i, t) option remember; n=0 or i>0 and t>0
%p A004869       and (b(n, i-1, t) or i^7<=n and b(n-i^7, i, t-1))
%p A004869     end:
%p A004869 a:= proc(n) option remember; local k;
%p A004869       for k from 1+ `if`(n=1, -1, a(n-1))
%p A004869       while not b(k, iroot(k, 7), 7) do od; k
%p A004869     end:
%p A004869 seq(a(n), n=1..60);  # _Alois P. Heinz_, Sep 16 2016
%t A004869 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 A004869 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 A004869 a[n_] := A[n, 7];
%t A004869 Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, May 20 2022, after _Alois P. Heinz_ in A336820 *)
%Y A004869 Column k=7 of A336820.
%K A004869 nonn
%O A004869 1,3
%A A004869 _N. J. A. Sloane_
%E A004869 More terms from _Alois P. Heinz_, Sep 16 2016