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A003341 Numbers that are the sum of 7 positive 4th powers.

%I A003341 #31 Feb 16 2025 08:32:27
%S A003341 7,22,37,52,67,82,87,97,102,112,117,132,147,162,167,177,182,197,212,
%T A003341 227,242,247,262,277,292,307,322,327,337,342,352,357,372,387,402,407,
%U A003341 417,422,437,452,467,482,487,502,517,532,547,562,567,577,582,592,597,612,627
%N A003341 Numbers that are the sum of 7 positive 4th powers.
%H A003341 Robert Israel, <a href="/A003341/b003341.txt">Table of n, a(n) for n = 1..10000</a>
%H A003341 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>.
%e A003341 From _David A. Corneth_, Aug 04 2020: (Start)
%e A003341 5971 is in the sequence as 5971 = 3^4 + 3^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4.
%e A003341 12022 is in the sequence as 12022 = 1^4 + 2^4 + 7^4 + 7^4 + 7^4 + 7^4 + 7^4.
%e A003341 16902 is in the sequence as 16902 = 1^4 + 1^4 + 3^4 + 6^4 + 7^4 + 9^4 + 9^4. (End)
%p A003341 N:= 1000:
%p A003341 S1:= {seq(i^4,i=1..floor(N^(1/4)))}:
%p A003341 S2:= select(`<=`,{seq(seq(i+j,i=S1),j=S1)},N):
%p A003341 S4:= select(`<=`,{seq(seq(i+j,i=S2),j=S2)},N):
%p A003341 S6:= select(`<=`,{seq(seq(i+j,i=S2),j=S4)},N):
%p A003341 sort(convert(select(`<=`,{seq(seq(i+j,i=S1),j=S6)},N),list)); # _Robert Israel_, Jul 21 2019
%o A003341 (Python)
%o A003341 from itertools import combinations_with_replacement as mc
%o A003341 def aupto(limit):
%o A003341     qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 6 <= limit]
%o A003341     ss = set(sum(c) for c in mc(qd, 7))
%o A003341     return sorted(s for s in ss if s <= limit)
%o A003341 print(aupto(630)) # _Michael S. Branicky_, Jul 22 2021
%Y A003341 Cf. A000583, A003330, A003340, A003342, A003352, A047718, A345568, A345823.
%K A003341 nonn,easy
%O A003341 1,1
%A A003341 _N. J. A. Sloane_