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%I #6 Jul 31 2021 16:17:10
%S 926372,952653,993573,1133343,1414591,1431366,1431397,1447327,1597928,
%T 1637020,1663391,1697685,1876624,1933329,1992377,1993376,1993666,
%U 2033328,2091879,2175912,2182160,2231110,2280544,2280575,2280786,2281567,2283668,2329602,2345563
%N Numbers that are the sum of eight fifth powers in five or more ways.
%H Sean A. Irvine, <a href="/A345613/b345613.txt">Table of n, a(n) for n = 1..10000</a>
%e 952653 is a term because 952653 = 2^5 + 2^5 + 6^5 + 7^5 + 9^5 + 12^5 + 12^5 + 13^5 = 2^5 + 2^5 + 7^5 + 7^5 + 9^5 + 11^5 + 11^5 + 14^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 + 15^5 = 3^5 + 4^5 + 4^5 + 6^5 + 10^5 + 10^5 + 13^5 + 13^5 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 + 15^5.
%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, 8):
%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. A345580, A345608, A345612, A345614, A345622, A346330.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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