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A345185 Numbers that are the sum of five third powers in nine or more ways.

%I A345185 #6 Aug 05 2021 15:25:51
%S A345185 5860,6112,6138,6462,6497,6588,6651,6859,6947,7001,7038,7057,7064,
%T A345185 7099,7190,7316,7328,7372,7433,7561,7587,7703,7759,7841,7902,8056,
%U A345185 8163,8289,8352,8371,8443,8506,8560,8569,8630,8632,8758,8928,8991,9017,9045,9080,9099
%N A345185 Numbers that are the sum of five third powers in nine or more ways.
%H A345185 David Consiglio, Jr., <a href="/A345185/b345185.txt">Table of n, a(n) for n = 1..10000</a>
%e A345185 6112 is a term because 6112 = 1^3 + 2^3 + 9^3 + 11^3 + 14^3  = 1^3 + 3^3 + 7^3 + 12^3 + 14^3  = 1^3 + 6^3 + 6^3 + 7^3 + 16^3  = 2^3 + 2^3 + 9^3 + 9^3 + 15^3  = 2^3 + 3^3 + 5^3 + 11^3 + 15^3  = 2^3 + 8^3 + 9^3 + 9^3 + 14^3  = 3^3 + 3^3 + 3^3 + 4^3 + 17^3  = 3^3 + 5^3 + 8^3 + 11^3 + 14^3  = 8^3 + 8^3 + 8^3 + 11^3 + 12^3.
%o A345185 (Python)
%o A345185 from itertools import combinations_with_replacement as cwr
%o A345185 from collections import defaultdict
%o A345185 keep = defaultdict(lambda: 0)
%o A345185 power_terms = [x**3 for x in range(1, 1000)]
%o A345185 for pos in cwr(power_terms, 5):
%o A345185     tot = sum(pos)
%o A345185     keep[tot] += 1
%o A345185 rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345185 for x in range(len(rets)):
%o A345185     print(rets[x])
%Y A345185 Cf. A341891, A344802, A345146, A345183, A345186, A345187, A345518.
%K A345185 nonn
%O A345185 1,1
%A A345185 _David Consiglio, Jr._, Jun 10 2021