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A345847 Numbers that are the sum of nine fourth powers in exactly five ways.

%I A345847 #6 Jul 31 2021 21:28:25
%S A345847 3189,4149,4229,4244,4309,4374,4404,4419,4549,4659,4724,4853,4899,
%T A345847 5028,5093,5139,5189,5204,5269,5284,5349,5379,5414,5509,5574,5619,
%U A345847 5634,5654,5684,5749,5814,5829,5939,6068,6133,6179,6308,6419,6564,6594,6614,6644,6709
%N A345847 Numbers that are the sum of nine fourth powers in exactly five ways.
%C A345847 Differs from A345589 at term 9 because 4469 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 8^4  = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4  = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 8^4  = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4  = 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4  = 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4.
%H A345847 Sean A. Irvine, <a href="/A345847/b345847.txt">Table of n, a(n) for n = 1..10000</a>
%e A345847 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 A345847 (Python)
%o A345847 from itertools import combinations_with_replacement as cwr
%o A345847 from collections import defaultdict
%o A345847 keep = defaultdict(lambda: 0)
%o A345847 power_terms = [x**4 for x in range(1, 1000)]
%o A345847 for pos in cwr(power_terms, 9):
%o A345847     tot = sum(pos)
%o A345847     keep[tot] += 1
%o A345847     rets = sorted([k for k, v in keep.items() if v == 5])
%o A345847     for x in range(len(rets)):
%o A345847         print(rets[x])
%Y A345847 Cf. A345589, A345797, A345837, A345846, A345848, A345857, A346340.
%K A345847 nonn
%O A345847 1,1
%A A345847 _David Consiglio, Jr._, Jun 26 2021