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%I #6 Jul 31 2021 16:09:53
%S 4157156,4492410,4510461,4915538,4948274,5005474,5015506,5179747,
%T 5219655,5252477,5739988,5756794,6323426,6326519,6382443,6423394,
%U 6654999,6705284,6793170,6861218,7101038,7147645,7147656,7148679,7266240,7280391,7283268,7314187,7413493
%N Numbers that are the sum of nine fifth powers in ten or more ways.
%H Sean A. Irvine, <a href="/A345627/b345627.txt">Table of n, a(n) for n = 1..10000</a>
%e 4492410 is a term because 4492410 = 1^5 + 1^5 + 2^5 + 3^5 + 5^5 + 7^5 + 7^5 + 13^5 + 21^5 = 1^5 + 2^5 + 6^5 + 10^5 + 11^5 + 11^5 + 14^5 + 16^5 + 19^5 = 1^5 + 6^5 + 7^5 + 8^5 + 9^5 + 9^5 + 14^5 + 18^5 + 18^5 = 2^5 + 5^5 + 6^5 + 6^5 + 7^5 + 15^5 + 15^5 + 16^5 + 18^5 = 2^5 + 5^5 + 6^5 + 10^5 + 10^5 + 11^5 + 11^5 + 15^5 + 20^5 = 3^5 + 3^5 + 7^5 + 7^5 + 9^5 + 12^5 + 13^5 + 18^5 + 18^5 = 3^5 + 3^5 + 8^5 + 8^5 + 8^5 + 12^5 + 12^5 + 17^5 + 19^5 = 3^5 + 4^5 + 6^5 + 7^5 + 8^5 + 13^5 + 14^5 + 16^5 + 19^5 = 4^5 + 4^5 + 4^5 + 7^5 + 11^5 + 11^5 + 13^5 + 18^5 + 18^5 = 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 9^5 + 16^5 + 17^5 + 18^5.
%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, 9):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 10])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345594, A345618, A345626, A345642, A346345.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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