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%I #6 Jul 31 2021 18:05:16
%S 21251,37811,38051,43251,43571,43875,44115,44531,45155,45651,45891,
%T 47411,47586,48276,49796,49971,52195,53235,53315,54131,56290,57395,
%U 57460,57570,58035,58500,59075,59330,59780,59795,59811,59860,60035,62180,62211,63971,66340
%N Numbers that are the sum of six fourth powers in six or more ways.
%H Sean A. Irvine, <a href="/A345563/b345563.txt">Table of n, a(n) for n = 1..10000</a>
%e 37811 is a term because 37811 = 1^4 + 2^4 + 2^4 + 7^4 + 11^4 + 12^4 = 2^4 + 2^4 + 4^4 + 7^4 + 9^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 9^4 + 13^4 = 3^4 + 4^4 + 8^4 + 8^4 + 11^4 + 11^4 = 4^4 + 6^4 + 7^4 + 9^4 + 9^4 + 12^4 = 5^4 + 5^4 + 9^4 + 10^4 + 10^4 + 10^4.
%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 >= 6])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A344940, A345515, A345562, A345564, A345572, A345720, A345818.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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