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A345521 Numbers that are the sum of seven cubes in three or more ways.

%I A345521 #7 Aug 05 2021 15:22:18
%S A345521 222,229,248,255,262,281,283,285,318,346,370,374,377,379,381,396,400,
%T A345521 407,412,419,426,433,437,438,444,451,463,470,472,475,477,489,494,496,
%U A345521 501,503,505,507,510,522,529,533,536,559,564,566,568,570,577,578,584,585
%N A345521 Numbers that are the sum of seven cubes in three or more ways.
%H A345521 Sean A. Irvine, <a href="/A345521/b345521.txt">Table of n, a(n) for n = 1..10000</a>
%e A345521 229 is a term because 229 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.
%o A345521 (Python)
%o A345521 from itertools import combinations_with_replacement as cwr
%o A345521 from collections import defaultdict
%o A345521 keep = defaultdict(lambda: 0)
%o A345521 power_terms = [x**3 for x in range(1, 1000)]
%o A345521 for pos in cwr(power_terms, 7):
%o A345521     tot = sum(pos)
%o A345521     keep[tot] += 1
%o A345521     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345521     for x in range(len(rets)):
%o A345521         print(rets[x])
%Y A345521 Cf. A345480, A345512, A345520, A345522, A345533, A345569, A345775.
%K A345521 nonn
%O A345521 1,1
%A A345521 _David Consiglio, Jr._, Jun 20 2021