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A345641 Numbers that are the sum of ten fifth powers in nine or more ways.

%I A345641 #6 Jul 31 2021 15:58:56
%S A345641 1192180,1226654,1242437,1431399,1431430,1431641,1431672,1431883,
%T A345641 1432453,1432664,1434765,1439174,1439416,1441695,1442718,1447602,
%U A345641 1448447,1455346,1455377,1464166,1464377,1464408,1474431,1474462,1475485,1491978,1497619,1505660,1531398
%N A345641 Numbers that are the sum of ten fifth powers in nine or more ways.
%H A345641 Sean A. Irvine, <a href="/A345641/b345641.txt">Table of n, a(n) for n = 1..1000</a>
%e A345641 1226654 is a term because 1226654 = 1^5 + 1^5 + 4^5 + 5^5 + 7^5 + 8^5 + 9^5 + 13^5 + 13^5 + 13^5 = 1^5 + 1^5 + 5^5 + 7^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 = 1^5 + 2^5 + 2^5 + 4^5 + 6^5 + 10^5 + 12^5 + 12^5 + 12^5 + 13^5 = 1^5 + 2^5 + 2^5 + 4^5 + 7^5 + 10^5 + 11^5 + 11^5 + 12^5 + 14^5 = 1^5 + 3^5 + 3^5 + 3^5 + 7^5 + 10^5 + 10^5 + 10^5 + 13^5 + 14^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 7^5 + 8^5 + 12^5 + 13^5 + 14^5 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 5^5 + 10^5 + 13^5 + 13^5 + 13^5 = 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5 + 8^5 + 9^5 + 16^5 = 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 8^5 + 9^5 + 16^5.
%o A345641 (Python)
%o A345641 from itertools import combinations_with_replacement as cwr
%o A345641 from collections import defaultdict
%o A345641 keep = defaultdict(lambda: 0)
%o A345641 power_terms = [x**5 for x in range(1, 1000)]
%o A345641 for pos in cwr(power_terms, 10):
%o A345641     tot = sum(pos)
%o A345641     keep[tot] += 1
%o A345641     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345641     for x in range(len(rets)):
%o A345641         print(rets[x])
%Y A345641 Cf. A345602, A345626, A345640, A345642, A346354.
%K A345641 nonn
%O A345641 1,1
%A A345641 _David Consiglio, Jr._, Jun 20 2021