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A345519 Numbers that are the sum of six cubes in ten or more ways.

%I A345519 #12 Jan 05 2024 13:18:13
%S A345519 3104,3215,3222,3267,3313,3339,3374,3430,3465,3491,3493,3528,3547,
%T A345519 3584,3645,3654,3698,3708,3736,3745,3752,3754,3761,3771,3780,3789,
%U A345519 3817,3824,3843,3862,3869,3878,3880,3888,3906,3915,3923,3943,3950,3969,3995,4004,4014
%N A345519 Numbers that are the sum of six cubes in ten or more ways.
%H A345519 Sean A. Irvine, <a href="/A345519/b345519.txt">Table of n, a(n) for n = 1..10000</a>
%e A345519 3215 is a term because 3215 = 1^3 + 1^3 + 1^3 + 4^3 + 6^3 + 13^3 = 1^3 + 1^3 + 2^3 + 2^3 + 9^3 + 12^3 = 1^3 + 1^3 + 3^3 + 8^3 + 8^3 + 11^3 = 1^3 + 2^3 + 3^3 + 5^3 + 8^3 + 12^3 = 1^3 + 3^3 + 3^3 + 3^3 + 10^3 + 11^3 = 1^3 + 3^3 + 8^3 + 8^3 + 8^3 + 9^3 = 2^3 + 3^3 + 6^3 + 6^3 + 8^3 + 11^3 = 3^3 + 3^3 + 3^3 + 8^3 + 9^3 + 10^3 = 3^3 + 5^3 + 5^3 + 5^3 + 6^3 + 12^3 = 6^3 + 6^3 + 6^3 + 6^3 + 7^3 + 10^3.
%o A345519 (Python)
%o A345519 from itertools import combinations_with_replacement as cwr
%o A345519 from collections import defaultdict
%o A345519 keep = defaultdict(lambda: 0)
%o A345519 power_terms = [x**3 for x in range(1, 1000)]
%o A345519 for pos in cwr(power_terms, 6):
%o A345519     tot = sum(pos)
%o A345519     keep[tot] += 1
%o A345519     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345519     for x in range(len(rets)):
%o A345519         print(rets[x])
%Y A345519 Cf. A345187, A345477, A345506, A345518, A345567, A345772.
%K A345519 nonn
%O A345519 1,1
%A A345519 _David Consiglio, Jr._, Jun 20 2021