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A346340 Numbers that are the sum of nine fifth powers in exactly five ways.

%I A346340 #6 Jul 31 2021 19:00:57
%S A346340 392063,392274,406559,458875,519237,538291,607947,663871,672024,
%T A346340 672055,672266,672297,673586,673797,674578,675390,680041,681330,
%U A346340 704582,704822,714299,730260,732603,763027,763324,765873,766417,777820,780099,814082,820887,825678
%N A346340 Numbers that are the sum of nine fifth powers in exactly five ways.
%C A346340 Differs from A345622 at term 50 because 926404 = 2^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 10^5 + 15^5 = 2^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 10^5 + 15^5 = 2^5 + 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 2^5 + 7^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 2^5 + 6^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5 = 1^5 + 1^5 + 4^5 + 4^5 + 7^5 + 11^5 + 12^5 + 12^5 + 12^5.
%H A346340 Sean A. Irvine, <a href="/A346340/b346340.txt">Table of n, a(n) for n = 1..10000</a>
%e A346340 392063 is a term because 392063 = 2^5 + 2^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 2^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 1^5 + 1^5 + 1^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5.
%o A346340 (Python)
%o A346340 from itertools import combinations_with_replacement as cwr
%o A346340 from collections import defaultdict
%o A346340 keep = defaultdict(lambda: 0)
%o A346340 power_terms = [x**5 for x in range(1, 1000)]
%o A346340 for pos in cwr(power_terms, 9):
%o A346340     tot = sum(pos)
%o A346340     keep[tot] += 1
%o A346340     rets = sorted([k for k, v in keep.items() if v == 5])
%o A346340     for x in range(len(rets)):
%o A346340         print(rets[x])
%Y A346340 Cf. A345622, A345847, A346330, A346339, A346341, A346350.
%K A346340 nonn
%O A346340 1,1
%A A346340 _David Consiglio, Jr._, Jul 13 2021