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A345622 Numbers that are the sum of nine fifth powers in five or more ways.

%I A345622 #6 Jul 31 2021 16:09:06
%S A345622 392063,392274,406559,458875,519237,538291,607947,663871,672024,
%T A345622 672055,672266,672297,673586,673797,674578,675390,680041,681330,
%U A345622 704582,704822,714299,730260,732603,763027,763324,765873,766417,777820,780099,814082,820887,825678
%N A345622 Numbers that are the sum of nine fifth powers in five or more ways.
%H A345622 Sean A. Irvine, <a href="/A345622/b345622.txt">Table of n, a(n) for n = 1..10000</a>
%e A345622 392274 is a term because 392274 = 1^5 + 1^5 + 4^5 + 4^5 + 7^5 + 8^5 + 8^5 + 9^5 + 12^5 = 1^5 + 3^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 2^5 + 3^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 3^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 2^5 + 3^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5.
%o A345622 (Python)
%o A345622 from itertools import combinations_with_replacement as cwr
%o A345622 from collections import defaultdict
%o A345622 keep = defaultdict(lambda: 0)
%o A345622 power_terms = [x**5 for x in range(1, 1000)]
%o A345622 for pos in cwr(power_terms, 9):
%o A345622     tot = sum(pos)
%o A345622     keep[tot] += 1
%o A345622     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A345622     for x in range(len(rets)):
%o A345622         print(rets[x])
%Y A345622 Cf. A345589, A345613, A345621, A345623, A345637, A346340.
%K A345622 nonn
%O A345622 1,1
%A A345622 _David Consiglio, Jr._, Jun 20 2021