%I #6 Jul 31 2021 18:05:10
%S 15395,16610,18866,19235,19410,20996,21011,21251,21316,21331,21491,
%T 21620,23811,25091,29700,29715,29906,29955,30356,30995,31235,31266,
%U 31331,31506,32035,33651,33795,33891,35171,35411,35636,35796,35971,37811,37971,38051,38595
%N Numbers that are the sum of six fourth powers in five or more ways.
%H Sean A. Irvine, <a href="/A345562/b345562.txt">Table of n, a(n) for n = 1..10000</a>
%e 16610 is a term because 16610 = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 10^4 = 2^4 + 2^4 + 2^4 + 5^4 + 6^4 + 11^4 = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 10^4 = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.
%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 >= 5])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A344358, A345514, A345561, A345563, A345571, A345719, A345817.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
