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%I #6 Aug 05 2021 15:23:53
%S 626,830,837,856,873,891,947,954,982,1008,1026,1045,1052,1053,1071,
%T 1094,1097,1106,1109,1134,1143,1150,1153,1169,1172,1195,1208,1227,
%U 1234,1241,1253,1260,1267,1278,1279,1283,1286,1290,1297,1316,1323,1324,1358,1361,1368
%N Numbers that are the sum of six cubes in four or more ways.
%H Sean A. Irvine, <a href="/A345513/b345513.txt">Table of n, a(n) for n = 1..10000</a>
%e 830 is a term because 830 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 8^3 = 1^3 + 3^3 + 3^3 + 5^3 + 5^3 + 6^3 = 1^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 = 2^3 + 2^3 + 3^3 + 3^3 + 6^3 + 6^3.
%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 >= 4])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A344034, A344808, A345512, A345514, A345522, A345561, A345766.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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