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A345554 Numbers that are the sum of ten cubes in six or more ways.

%I A345554 #6 Aug 05 2021 15:16:53
%S A345554 436,440,447,466,473,477,480,492,499,503,506,508,510,513,515,518,525,
%T A345554 527,529,532,534,536,538,539,541,551,553,560,562,564,567,569,571,577,
%U A345554 581,584,588,590,595,597,599,601,602,603,604,606,607,608,613,614,616,618
%N A345554 Numbers that are the sum of ten cubes in six or more ways.
%H A345554 Sean A. Irvine, <a href="/A345554/b345554.txt">Table of n, a(n) for n = 1..10000</a>
%e A345554 440 is a term because 440 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 5^3 = 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3.
%o A345554 (Python)
%o A345554 from itertools import combinations_with_replacement as cwr
%o A345554 from collections import defaultdict
%o A345554 keep = defaultdict(lambda: 0)
%o A345554 power_terms = [x**3 for x in range(1, 1000)]
%o A345554 for pos in cwr(power_terms, 10):
%o A345554     tot = sum(pos)
%o A345554     keep[tot] += 1
%o A345554     rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345554     for x in range(len(rets)):
%o A345554         print(rets[x])
%Y A345554 Cf. A345545, A345553, A345555, A345599, A345808, A346805.
%K A345554 nonn
%O A345554 1,1
%A A345554 _David Consiglio, Jr._, Jun 20 2021