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%I #6 Aug 05 2021 15:23:56
%S 1045,1169,1241,1260,1377,1384,1432,1440,1488,1495,1530,1539,1549,
%T 1556,1558,1584,1586,1594,1595,1602,1612,1617,1640,1647,1654,1657,
%U 1673,1675,1677,1703,1710,1712,1715,1719,1729,1736,1738,1745,1747,1754,1764,1766,1771
%N Numbers that are the sum of six cubes in five or more ways.
%H Sean A. Irvine, <a href="/A345514/b345514.txt">Table of n, a(n) for n = 1..10000</a>
%e 1169 is a term because 1169 = 1^3 + 2^3 + 2^3 + 3^3 + 4^3 + 9^3 = 1^3 + 2^3 + 5^3 + 5^3 + 5^3 + 7^3 = 1^3 + 3^3 + 4^3 + 4^3 + 4^3 + 8^3 = 2^3 + 3^3 + 3^3 + 4^3 + 5^3 + 8^3 = 3^3 + 3^3 + 3^3 + 3^3 + 7^3 + 7^3.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**3 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 6):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 5])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A343989, A344809, A345513, A345515, A345523, A345562, A345767.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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