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A344243 Numbers that are the sum of five fourth powers in three or more ways.

%I A344243 #12 May 10 2024 02:19:44
%S A344243 4225,6610,6850,9170,9235,9490,11299,12929,14209,14690,14755,14770,
%T A344243 15314,16579,16594,16659,16834,17203,17235,17315,17859,17874,17939,
%U A344243 18785,18850,18979,19154,19700,19715,20674,20995,21235,21250,21330,21364,21410,21954,23139,23795,24754,25810,26578,28610,28930
%N A344243 Numbers that are the sum of five fourth powers in three or more ways.
%H A344243 David Consiglio, Jr., <a href="/A344243/b344243.txt">Table of n, a(n) for n = 1..20000</a>
%e A344243 6850 = 1^4 + 2^4 + 2^4 + 4^4 + 9^4
%e A344243      = 2^4 + 3^4 + 4^4 + 7^4 + 8^4
%e A344243      = 3^4 + 3^4 + 6^4 + 6^4 + 8^4
%e A344243 so 6850 is a term of this sequence.
%o A344243 (Python)
%o A344243 from itertools import combinations_with_replacement as cwr
%o A344243 from collections import defaultdict
%o A344243 keep = defaultdict(lambda: 0)
%o A344243 power_terms = [x**4 for x in range(1,50)]
%o A344243 for pos in cwr(power_terms,5):
%o A344243     tot = sum(pos)
%o A344243     keep[tot] += 1
%o A344243 rets = sorted([k for k,v in keep.items() if v >= 3])
%o A344243 for x in range(len(rets)):
%o A344243     print(rets[x])
%Y A344243 Cf. A342687, A343704, A344238, A344241, A344244, A344354, A345560.
%K A344243 nonn
%O A344243 1,1
%A A344243 _David Consiglio, Jr._, May 12 2021