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A345565 Numbers that are the sum of six fourth powers in eight or more ways.

%I A345565 #6 Jul 31 2021 18:05:23
%S A345565 58035,59780,87746,88595,96195,96450,102371,106451,106515,108035,
%T A345565 108275,108290,108771,112370,112931,115251,122835,122850,122915,
%U A345565 124691,125971,132546,133395,133571,133586,134675,134931,136931,138275,138595,143650,144755,144835
%N A345565 Numbers that are the sum of six fourth powers in eight or more ways.
%H A345565 Sean A. Irvine, <a href="/A345565/b345565.txt">Table of n, a(n) for n = 1..10000</a>
%e A345565 59780 is a term because 59780 = 1^4 + 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 1^4 + 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 1^4 + 7^4 + 7^4 + 9^4 + 10^4 + 14^4 = 2^4 + 5^4 + 6^4 + 11^4 + 11^4 + 13^4 = 3^4 + 7^4 + 8^4 + 10^4 + 11^4 + 13^4 = 5^4 + 6^4 + 7^4 + 7^4 + 11^4 + 14^4.
%o A345565 (Python)
%o A345565 from itertools import combinations_with_replacement as cwr
%o A345565 from collections import defaultdict
%o A345565 keep = defaultdict(lambda: 0)
%o A345565 power_terms = [x**4 for x in range(1, 1000)]
%o A345565 for pos in cwr(power_terms, 6):
%o A345565     tot = sum(pos)
%o A345565     keep[tot] += 1
%o A345565     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345565     for x in range(len(rets)):
%o A345565         print(rets[x])
%Y A345565 Cf. A344944, A345517, A345564, A345566, A345574, A345722, A345820.
%K A345565 nonn
%O A345565 1,1
%A A345565 _David Consiglio, Jr._, Jun 20 2021