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A345606 Numbers that are the sum of seven fifth powers in three or more ways.

%I A345606 #6 Jul 31 2021 16:25:09
%S A345606 84457,166997,324860,326199,358482,359327,391007,391999,408158,455146,
%T A345606 455749,486468,502429,572054,595519,614505,622280,648319,671210,
%U A345606 672022,696468,696499,696710,697491,699592,704243,713274,729235,755516,796467,857518,877645
%N A345606 Numbers that are the sum of seven fifth powers in three or more ways.
%H A345606 Sean A. Irvine, <a href="/A345606/b345606.txt">Table of n, a(n) for n = 1..10000</a>
%e A345606 166997 is a term because 166997 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 = 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 10^5 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 10^5.
%o A345606 (Python)
%o A345606 from itertools import combinations_with_replacement as cwr
%o A345606 from collections import defaultdict
%o A345606 keep = defaultdict(lambda: 0)
%o A345606 power_terms = [x**5 for x in range(1, 1000)]
%o A345606 for pos in cwr(power_terms, 7):
%o A345606     tot = sum(pos)
%o A345606     keep[tot] += 1
%o A345606     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345606     for x in range(len(rets)):
%o A345606         print(rets[x])
%Y A345606 Cf. A345569, A345604, A345605, A345607, A345611, A346280.
%K A345606 nonn
%O A345606 1,1
%A A345606 _David Consiglio, Jr._, Jun 20 2021