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A345590 Numbers that are the sum of nine fourth powers in six or more ways.

%I A345590 #6 Jul 31 2021 17:39:01
%S A345590 4469,4484,5444,5459,5524,5589,5699,5764,6629,6659,6674,6694,6724,
%T A345590 6739,6789,6804,6854,6869,6884,6899,6914,6934,6949,6964,6979,7014,
%U A345590 7029,7044,7094,7109,7154,7219,7269,7284,7334,7348,7349,7413,7459,7478,7494,7523,7524
%N A345590 Numbers that are the sum of nine fourth powers in six or more ways.
%H A345590 Sean A. Irvine, <a href="/A345590/b345590.txt">Table of n, a(n) for n = 1..10000</a>
%e A345590 4484 is a term because 4484 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4.
%o A345590 (Python)
%o A345590 from itertools import combinations_with_replacement as cwr
%o A345590 from collections import defaultdict
%o A345590 keep = defaultdict(lambda: 0)
%o A345590 power_terms = [x**4 for x in range(1, 1000)]
%o A345590 for pos in cwr(power_terms, 9):
%o A345590     tot = sum(pos)
%o A345590     keep[tot] += 1
%o A345590     rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345590     for x in range(len(rets)):
%o A345590         print(rets[x])
%Y A345590 Cf. A345545, A345581, A345589, A345591, A345599, A345623, A345848.
%K A345590 nonn
%O A345590 1,1
%A A345590 _David Consiglio, Jr._, Jun 20 2021