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A345781 Numbers that are the sum of seven cubes in exactly nine ways.

%I A345781 #6 Jul 31 2021 22:39:34
%S A345781 1496,1648,1720,1737,1772,1781,1802,1835,1844,1882,1891,1898,1900,
%T A345781 1907,1912,1919,1945,1952,1954,1961,1996,2000,2012,2026,2071,2080,
%U A345781 2098,2107,2110,2115,2116,2132,2134,2136,2139,2150,2152,2168,2178,2185,2187,2195,2205
%N A345781 Numbers that are the sum of seven cubes in exactly nine ways.
%C A345781 Differs from A345527 at term 3 because 1704 = 1^3 + 1^3 + 1^3 + 3^3 + 6^3 + 9^3 + 9^3  = 1^3 + 1^3 + 1^3 + 4^3 + 5^3 + 8^3 + 10^3  = 1^3 + 1^3 + 2^3 + 2^3 + 7^3 + 7^3 + 10^3  = 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 6^3 + 11^3  = 1^3 + 2^3 + 4^3 + 6^3 + 7^3 + 7^3 + 9^3  = 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 6^3 + 11^3  = 2^3 + 2^3 + 3^3 + 5^3 + 8^3 + 8^3 + 8^3  = 3^3 + 3^3 + 3^3 + 4^3 + 6^3 + 7^3 + 10^3  = 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 9^3 + 9^3  = 3^3 + 6^3 + 6^3 + 6^3 + 7^3 + 7^3 + 7^3.
%C A345781 Likely finite.
%H A345781 Sean A. Irvine, <a href="/A345781/b345781.txt">Table of n, a(n) for n = 1..338</a>
%e A345781 1648 is a term because 1648 = 1^3 + 1^3 + 1^3 + 2^3 + 4^3 + 7^3 + 9^3 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 10^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 10^3 = 1^3 + 1^3 + 3^3 + 4^3 + 5^3 + 7^3 + 8^3 = 1^3 + 2^3 + 2^3 + 5^3 + 6^3 + 6^3 + 8^3 = 1^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 + 9^3 = 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 6^3 + 9^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 8^3 + 8^3 = 3^3 + 3^3 + 3^3 + 5^3 + 5^3 + 7^3 + 7^3.
%o A345781 (Python)
%o A345781 from itertools import combinations_with_replacement as cwr
%o A345781 from collections import defaultdict
%o A345781 keep = defaultdict(lambda: 0)
%o A345781 power_terms = [x**3 for x in range(1, 1000)]
%o A345781 for pos in cwr(power_terms, 7):
%o A345781     tot = sum(pos)
%o A345781     keep[tot] += 1
%o A345781     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345781     for x in range(len(rets)):
%o A345781         print(rets[x])
%Y A345781 Cf. A345527, A345771, A345780, A345782, A345791, A345831.
%K A345781 nonn
%O A345781 1,1
%A A345781 _David Consiglio, Jr._, Jun 26 2021