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A345801 Numbers that are the sum of nine cubes in exactly nine ways.

%I A345801 #6 Jul 31 2021 22:33:02
%S A345801 859,861,896,903,922,929,935,939,959,973,997,999,1009,1016,1020,1023,
%T A345801 1027,1029,1030,1034,1035,1036,1037,1041,1046,1059,1060,1064,1065,
%U A345801 1066,1067,1071,1072,1079,1086,1091,1105,1116,1131,1138,1146,1152,1155,1157,1158
%N A345801 Numbers that are the sum of nine cubes in exactly nine ways.
%C A345801 Differs from A345548 at term 10 because 966 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 6^3 + 9^3  = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 + 8^3  = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 9^3  = 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 + 5^3 + 6^3 + 7^3  = 1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 + 6^3 + 7^3  = 1^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 8^3  = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3 + 9^3  = 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 5^3 + 5^3 + 6^3 + 7^3  = 2^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 7^3 + 7^3  = 3^3 + 4^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3.
%C A345801 Likely finite.
%H A345801 Sean A. Irvine, <a href="/A345801/b345801.txt">Table of n, a(n) for n = 1..86</a>
%e A345801 861 is a term because 861 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 8^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 5^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 6^3 = 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 8^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 = 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3.
%o A345801 (Python)
%o A345801 from itertools import combinations_with_replacement as cwr
%o A345801 from collections import defaultdict
%o A345801 keep = defaultdict(lambda: 0)
%o A345801 power_terms = [x**3 for x in range(1, 1000)]
%o A345801 for pos in cwr(power_terms, 9):
%o A345801     tot = sum(pos)
%o A345801     keep[tot] += 1
%o A345801     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345801     for x in range(len(rets)):
%o A345801         print(rets[x])
%Y A345801 Cf. A345548, A345791, A345800, A345802, A345811, A345851.
%K A345801 nonn
%O A345801 1,1
%A A345801 _David Consiglio, Jr._, Jun 26 2021