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A345780 Numbers that are the sum of seven cubes in exactly eight ways.

%I A345780 #6 Jul 31 2021 22:39:30
%S A345780 1385,1515,1552,1557,1585,1587,1603,1613,1622,1655,1665,1674,1681,
%T A345780 1718,1719,1739,1741,1746,1753,1755,1765,1767,1782,1793,1805,1809,
%U A345780 1811,1818,1819,1826,1828,1830,1833,1838,1856,1870,1873,1881,1901,1905,1931,1935,1937
%N A345780 Numbers that are the sum of seven cubes in exactly eight ways.
%C A345780 Differs from A345526 at term 2 because 1496 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 9^3 + 9^3  = 1^3 + 1^3 + 2^3 + 3^3 + 4^3 + 4^3 + 11^3  = 1^3 + 1^3 + 4^3 + 4^3 + 5^3 + 8^3 + 9^3  = 1^3 + 2^3 + 2^3 + 4^3 + 7^3 + 7^3 + 9^3  = 1^3 + 5^3 + 5^3 + 6^3 + 7^3 + 7^3 + 7^3  = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 11^3  = 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 + 10^3  = 2^3 + 3^3 + 6^3 + 6^3 + 7^3 + 7^3 + 7^3  = 4^3 + 4^3 + 4^3 + 4^3 + 6^3 + 8^3 + 8^3.
%C A345780 Likely finite.
%H A345780 Sean A. Irvine, <a href="/A345780/b345780.txt">Table of n, a(n) for n = 1..343</a>
%e A345780 1496 is a term because 1496 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 8^3 + 8^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 10^3 = 1^3 + 1^3 + 3^3 + 3^3 + 4^3 + 7^3 + 8^3 = 1^3 + 2^3 + 2^3 + 3^3 + 6^3 + 6^3 + 8^3 = 1^3 + 4^3 + 4^3 + 5^3 + 6^3 + 6^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 10^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 6^3 + 9^3 = 2^3 + 3^3 + 5^3 + 5^3 + 6^3 + 6^3 + 6^3 = 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 7^3 + 7^3.
%o A345780 (Python)
%o A345780 from itertools import combinations_with_replacement as cwr
%o A345780 from collections import defaultdict
%o A345780 keep = defaultdict(lambda: 0)
%o A345780 power_terms = [x**3 for x in range(1, 1000)]
%o A345780 for pos in cwr(power_terms, 7):
%o A345780     tot = sum(pos)
%o A345780     keep[tot] += 1
%o A345780     rets = sorted([k for k, v in keep.items() if v == 8])
%o A345780     for x in range(len(rets)):
%o A345780         print(rets[x])
%Y A345780 Cf. A345526, A345770, A345779, A345781, A345790, A345830.
%K A345780 nonn
%O A345780 1,1
%A A345780 _David Consiglio, Jr._, Jun 26 2021