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%I #6 Jul 31 2021 18:05:19
%S 21251,43875,48276,49796,53315,58035,58500,59780,59795,59811,67875,
%T 68306,69155,69779,71955,72051,72131,73970,74420,74851,77010,80291,
%U 80515,81875,82275,84515,86436,86451,86531,87075,87746,88355,88595,88660,88675,90355,91475
%N Numbers that are the sum of six fourth powers in seven or more ways.
%H Sean A. Irvine, <a href="/A345564/b345564.txt">Table of n, a(n) for n = 1..10000</a>
%e 43875 is a term because 43875 = 1^4 + 2^4 + 9^4 + 9^4 + 10^4 + 12^4 = 2^4 + 2^4 + 2^4 + 5^4 + 11^4 + 13^4 = 2^4 + 2^4 + 5^4 + 7^4 + 7^4 + 14^4 = 2^4 + 5^4 + 6^4 + 9^4 + 11^4 + 12^4 = 3^4 + 7^4 + 8^4 + 9^4 + 10^4 + 12^4 = 4^4 + 4^4 + 7^4 + 7^4 + 10^4 + 13^4 = 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**4 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 6):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 7])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A344942, A345516, A345563, A345565, A345573, A345721, A345819.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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