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A345552 Numbers that are the sum of ten cubes in four or more ways.

%I A345552 #6 Aug 05 2021 15:16:46
%S A345552 225,232,251,258,265,272,284,286,288,291,307,310,314,321,323,328,342,
%T A345552 347,349,356,363,366,373,375,377,380,382,384,389,391,398,399,401,403,
%U A345552 405,408,410,412,414,415,417,419,421,422,424,427,429,434,436,438,440,441
%N A345552 Numbers that are the sum of ten cubes in four or more ways.
%H A345552 Sean A. Irvine, <a href="/A345552/b345552.txt">Table of n, a(n) for n = 1..10000</a>
%e A345552 232 is a term because 232 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 = 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.
%o A345552 (Python)
%o A345552 from itertools import combinations_with_replacement as cwr
%o A345552 from collections import defaultdict
%o A345552 keep = defaultdict(lambda: 0)
%o A345552 power_terms = [x**3 for x in range(1, 1000)]
%o A345552 for pos in cwr(power_terms, 10):
%o A345552     tot = sum(pos)
%o A345552     keep[tot] += 1
%o A345552     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345552     for x in range(len(rets)):
%o A345552         print(rets[x])
%Y A345552 Cf. A345543, A345551, A345553, A345597, A345806.
%K A345552 nonn
%O A345552 1,1
%A A345552 _David Consiglio, Jr._, Jun 20 2021