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A346282 Numbers that are the sum of seven fifth powers in exactly five ways.

%I A346282 #6 Jul 31 2021 19:12:00
%S A346282 6768576,6776120,7883668,8625376,8740709,10036201,10604054,12476826,
%T A346282 12618493,13006575,13060213,13080706,13174250,13536416,13550162,
%U A346282 13662500,14110656,15169276,15247994,16053313,16060683,16374218,16573507,16600001,17735057,17749152
%N A346282 Numbers that are the sum of seven fifth powers in exactly five ways.
%C A346282 Differs from A345608 at term 16 because 13562501 = 1^5 + 1^5 + 1^5 + 9^5 + 14^5 + 20^5 + 25^5 = 1^5 + 15^5 + 15^5 + 15^5 + 15^5 + 15^5 + 25^5 = 6^5 + 7^5 + 11^5 + 16^5 + 18^5 + 19^5 + 24^5 = 7^5 + 7^5 + 11^5 + 13^5 + 19^5 + 21^5 + 23^5 = 2^5 + 6^5 + 14^5 + 18^5 + 18^5 + 21^5 + 22^5 = 1^5 + 5^5 + 15^5 + 20^5 + 20^5 + 20^5 + 20^5.
%H A346282 Sean A. Irvine, <a href="/A346282/b346282.txt">Table of n, a(n) for n = 1..10000</a>
%e A346282 6768576 is a term because 6768576 = 4^5 + 6^5 + 6^5 + 6^5 + 9^5 + 12^5 + 23^5 = 1^5 + 3^5 + 4^5 + 8^5 + 11^5 + 17^5 + 22^5 = 6^5 + 12^5 + 13^5 + 14^5 + 15^5 + 15^5 + 21^5 = 8^5 + 10^5 + 12^5 + 12^5 + 16^5 + 18^5 + 20^5 = 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 18^5 + 20^5.
%o A346282 (Python)
%o A346282 from itertools import combinations_with_replacement as cwr
%o A346282 from collections import defaultdict
%o A346282 keep = defaultdict(lambda: 0)
%o A346282 power_terms = [x**5 for x in range(1, 1000)]
%o A346282 for pos in cwr(power_terms, 7):
%o A346282     tot = sum(pos)
%o A346282     keep[tot] += 1
%o A346282     rets = sorted([k for k, v in keep.items() if v == 5])
%o A346282     for x in range(len(rets)):
%o A346282         print(rets[x])
%Y A346282 Cf. A345608, A345827, A346281, A346283, A346330, A346360.
%K A346282 nonn
%O A346282 1,1
%A A346282 _David Consiglio, Jr._, Jul 13 2021