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A003340 Numbers that are the sum of 6 positive 4th powers.

%I A003340 #37 Feb 16 2025 08:32:27
%S A003340 6,21,36,51,66,81,86,96,101,116,131,146,161,166,181,196,211,226,246,
%T A003340 261,276,291,306,321,326,336,341,356,371,386,401,406,421,436,451,466,
%U A003340 486,501,516,531,546,561,576,581,596,611,626,630,641,645,660,661,675,676,690
%N A003340 Numbers that are the sum of 6 positive 4th powers.
%H A003340 David A. Corneth, <a href="/A003340/b003340.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H A003340 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number.</a>
%e A003340 From _David A. Corneth_, Aug 04 2020: (Start)
%e A003340 13090 is in the sequence as 13090 = 4^4 + 4^4 + 5^4 + 6^4 + 8^4 + 9^4.
%e A003340 17539 is in the sequence as 17539 = 2^4 + 3^4 + 4^4 + 5^4 + 9^4 + 10^4.
%e A003340 23732 is in the sequence as 23732 = 3^4 + 5^4 + 5^4 + 7^4 + 10^4 + 10^4. (End)
%t A003340 Select[Range[1000], AnyTrue[PowersRepresentations[#, 6, 4], First[#]>0&]&] (* _Jean-François Alcover_, Jul 18 2017 *)
%o A003340 (Python)
%o A003340 from itertools import combinations_with_replacement as combs_with_rep
%o A003340 def aupto(limit):
%o A003340     qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 5 <= limit]
%o A003340     ss = set(sum(c) for c in combs_with_rep(qd, 6))
%o A003340     return sorted(s for s in ss if s <= limit)
%o A003340 print(aupto(700)) # _Michael S. Branicky_, Jun 21 2021
%Y A003340 Cf. A000583, A003329, A003339, A003341, A003351, A345559, A345813.
%K A003340 nonn,easy
%O A003340 1,1
%A A003340 _N. J. A. Sloane_