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A004843 Numbers that are the sum of at most 3 positive 5th powers.

%I A004843 #25 Oct 27 2023 21:04:45
%S A004843 0,1,2,3,32,33,34,64,65,96,243,244,245,275,276,307,486,487,518,729,
%T A004843 1024,1025,1026,1056,1057,1088,1267,1268,1299,1510,2048,2049,2080,
%U A004843 2291,3072,3125,3126,3127,3157,3158,3189,3368,3369,3400,3611,4149,4150,4181,4392
%N A004843 Numbers that are the sum of at most 3 positive 5th powers.
%H A004843 Alois P. Heinz, <a href="/A004843/b004843.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Vincenzo Librandi)
%p A004843 b:= proc(n, i, t) option remember; n=0 or i>0 and t>0
%p A004843       and (b(n, i-1, t) or i^5<=n and b(n-i^5, i, t-1))
%p A004843     end:
%p A004843 a:= proc(n) option remember; local k;
%p A004843       for k from 1+ `if`(n=1, -1, a(n-1))
%p A004843       while not b(k, iroot(k, 5), 3) do od; k
%p A004843     end:
%p A004843 seq(a(n), n=1..50);  # _Alois P. Heinz_, Sep 16 2016
%t A004843 Select[Table[n, {n, 0, 6000}], Length[PowersRepresentations[#, 3, 5]] > 0 &] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%Y A004843 Cf. A004842, A004845.
%K A004843 nonn
%O A004843 1,3
%A A004843 _N. J. A. Sloane_