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A345791 Numbers that are the sum of eight cubes in exactly nine ways.

%I A345791 #6 Jul 31 2021 22:37:30
%S A345791 984,1080,1136,1171,1192,1197,1204,1223,1269,1273,1280,1306,1318,1325,
%T A345791 1332,1333,1337,1344,1356,1360,1369,1370,1374,1377,1379,1404,1406,
%U A345791 1415,1416,1422,1425,1430,1432,1438,1442,1444,1445,1456,1476,1481,1486,1488,1494
%N A345791 Numbers that are the sum of eight cubes in exactly nine ways.
%C A345791 Differs from A345539 at term 5 because 1185 = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 4^3 + 4^3 + 10^3  = 1^3 + 1^3 + 1^3 + 4^3 + 6^3 + 6^3 + 7^3 + 7^3  = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 5^3 + 10^3  = 1^3 + 2^3 + 2^3 + 2^3 + 6^3 + 6^3 + 6^3 + 8^3  = 1^3 + 2^3 + 2^3 + 4^3 + 5^3 + 5^3 + 5^3 + 9^3  = 1^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 6^3 + 7^3  = 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 9^3  = 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 8^3 + 8^3  = 2^3 + 3^3 + 5^3 + 5^3 + 5^3 + 6^3 + 6^3 + 7^3  = 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 6^3 + 7^3 + 7^3.
%C A345791 Likely finite.
%H A345791 Sean A. Irvine, <a href="/A345791/b345791.txt">Table of n, a(n) for n = 1..146</a>
%e A345791 1080 is a term because 1080 = 1^3 + 1^3 + 1^3 + 2^3 + 4^3 + 5^3 + 5^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 9^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 8^3 = 1^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 8^3 = 1^3 + 3^3 + 3^3 + 4^3 + 4^3 + 5^3 + 5^3 + 6^3 = 1^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 7^3 = 2^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 + 6^3 = 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 5^3 + 5^3 + 6^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 5^3 + 7^3.
%o A345791 (Python)
%o A345791 from itertools import combinations_with_replacement as cwr
%o A345791 from collections import defaultdict
%o A345791 keep = defaultdict(lambda: 0)
%o A345791 power_terms = [x**3 for x in range(1, 1000)]
%o A345791 for pos in cwr(power_terms, 8):
%o A345791     tot = sum(pos)
%o A345791     keep[tot] += 1
%o A345791     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345791     for x in range(len(rets)):
%o A345791         print(rets[x])
%Y A345791 Cf. A345539, A345781, A345790, A345792, A345801, A345841.
%K A345791 nonn
%O A345791 1,1
%A A345791 _David Consiglio, Jr._, Jun 26 2021