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A346342 Numbers that are the sum of nine fifth powers in exactly seven ways.

%I A346342 #6 Jul 31 2021 19:01:04
%S A346342 1431429,1439173,1447570,1504636,1597929,1671167,1696159,1697686,
%T A346342 1697928,1778835,1936454,1975049,2017344,2092122,2182161,2198967,
%U A346342 2208680,2280818,2283911,2289343,2314335,2329845,2340319,2345806,2362370,2388651,2497771,2529407,2530672
%N A346342 Numbers that are the sum of nine fifth powers in exactly seven ways.
%C A346342 Differs from A345624 at term 1 because 1431398 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 12^5 + 16^5 = 1^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.
%H A346342 Sean A. Irvine, <a href="/A346342/b346342.txt">Table of n, a(n) for n = 1..10000</a>
%e A346342 1431398 is a term because 1431398 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 12^5 + 16^5 = 1^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.
%o A346342 (Python)
%o A346342 from itertools import combinations_with_replacement as cwr
%o A346342 from collections import defaultdict
%o A346342 keep = defaultdict(lambda: 0)
%o A346342 power_terms = [x**5 for x in range(1, 1000)]
%o A346342 for pos in cwr(power_terms, 9):
%o A346342     tot = sum(pos)
%o A346342     keep[tot] += 1
%o A346342     rets = sorted([k for k, v in keep.items() if v == 7])
%o A346342     for x in range(len(rets)):
%o A346342         print(rets[x])
%Y A346342 Cf. A345624, A345849, A346332, A346341, A346343, A346352.
%K A346342 nonn
%O A346342 1,1
%A A346342 _David Consiglio, Jr._, Jul 13 2021