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A346280 Numbers that are the sum of seven fifth powers in exactly three ways.

%I A346280 #6 Jul 31 2021 19:11:53
%S A346280 84457,166997,324860,326199,358482,359327,391007,391999,408158,455146,
%T A346280 455749,486468,502429,572054,595519,614505,622280,648319,671210,
%U A346280 672022,696468,696499,696710,697491,699592,704243,713274,729235,755516,796467,857518,877645
%N A346280 Numbers that are the sum of seven fifth powers in exactly three ways.
%C A346280 Differs from A345606 at term 39 because 893604 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 10^5 + 15^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5.
%H A346280 Sean A. Irvine, <a href="/A346280/b346280.txt">Table of n, a(n) for n = 1..10000</a>
%e A346280 84457 is a term because 84457 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5.
%o A346280 (Python)
%o A346280 from itertools import combinations_with_replacement as cwr
%o A346280 from collections import defaultdict
%o A346280 keep = defaultdict(lambda: 0)
%o A346280 power_terms = [x**5 for x in range(1, 1000)]
%o A346280 for pos in cwr(power_terms, 7):
%o A346280     tot = sum(pos)
%o A346280     keep[tot] += 1
%o A346280     rets = sorted([k for k, v in keep.items() if v == 3])
%o A346280     for x in range(len(rets)):
%o A346280         print(rets[x])
%Y A346280 Cf. A345606, A345825, A346279, A346281, A346328, A346358.
%K A346280 nonn
%O A346280 1,1
%A A346280 _David Consiglio, Jr._, Jul 13 2021