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A345589 Numbers that are the sum of nine fourth powers in five or more ways.

%I A345589 #6 Jul 31 2021 17:38:55
%S A345589 3189,4149,4229,4244,4309,4374,4404,4419,4469,4484,4549,4659,4724,
%T A345589 4853,4899,5028,5093,5139,5189,5204,5269,5284,5349,5379,5414,5444,
%U A345589 5459,5509,5524,5574,5589,5619,5634,5654,5684,5699,5749,5764,5814,5829,5939,6068,6133
%N A345589 Numbers that are the sum of nine fourth powers in five or more ways.
%H A345589 Sean A. Irvine, <a href="/A345589/b345589.txt">Table of n, a(n) for n = 1..10000</a>
%e A345589 4149 is a term because 4149 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 = 4^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4.
%o A345589 (Python)
%o A345589 from itertools import combinations_with_replacement as cwr
%o A345589 from collections import defaultdict
%o A345589 keep = defaultdict(lambda: 0)
%o A345589 power_terms = [x**4 for x in range(1, 1000)]
%o A345589 for pos in cwr(power_terms, 9):
%o A345589     tot = sum(pos)
%o A345589     keep[tot] += 1
%o A345589     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A345589     for x in range(len(rets)):
%o A345589         print(rets[x])
%Y A345589 Cf. A345544, A345580, A345588, A345590, A345598, A345622, A345847.
%K A345589 nonn
%O A345589 1,1
%A A345589 _David Consiglio, Jr._, Jun 20 2021