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%I #6 Jul 31 2021 15:58:17
%S 8194,21940,52419,52450,52481,52661,52692,52903,53442,53473,53684,
%T 54465,54520,54551,54582,54762,54793,55004,55543,55574,55691,55722,
%U 55785,55933,56566,56714,57644,57675,57886,58667,58815,60194,60225,60436,60768,61217,62295
%N Numbers that are the sum of ten fifth powers in three or more ways.
%H Sean A. Irvine, <a href="/A345635/b345635.txt">Table of n, a(n) for n = 1..10000</a>
%e 21940 is a term because 21940 = 1^5 + 2^5 + 2^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 = 1^5 + 3^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5 = 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5.
%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**5 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 10):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 3])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345596, A345620, A345634, A345636, A346348.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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