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A004845 Numbers that are the sum of at most 5 positive 5th powers.

%I A004845 #23 Oct 27 2023 20:59:12
%S A004845 0,1,2,3,4,5,32,33,34,35,36,64,65,66,67,96,97,98,128,129,160,243,244,
%T A004845 245,246,247,275,276,277,278,307,308,309,339,340,371,486,487,488,489,
%U A004845 518,519,520,550,551,582,729,730,731,761,762,793,972,973,1004,1024
%N A004845 Numbers that are the sum of at most 5 positive 5th powers.
%H A004845 Alois P. Heinz, <a href="/A004845/b004845.txt">Table of n, a(n) for n = 1..10000</a> (first 300 terms from Vincenzo Librandi)
%p A004845 b:= proc(n, i, t) option remember; n=0 or i>0 and t>0
%p A004845       and (b(n, i-1, t) or i^5<=n and b(n-i^5, i, t-1))
%p A004845     end:
%p A004845 a:= proc(n) option remember; local k;
%p A004845       for k from 1+ `if`(n=1, -1, a(n-1))
%p A004845       while not b(k, iroot(k, 5), 5) do od; k
%p A004845     end:
%p A004845 seq(a(n), n=1..50);  # _Alois P. Heinz_, Sep 16 2016
%t A004845 Select[Table[n, {n, 0, 1200}], Length[PowersRepresentations[#, 5, 5]] > 0 &] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%Y A004845 Column k=5 of A336820.
%K A004845 nonn
%O A004845 1,3
%A A004845 _N. J. A. Sloane_