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%I #6 Jul 31 2021 22:37:34
%S 1185,1243,1288,1295,1299,1386,1397,1400,1412,1423,1448,1449,1451,
%T 1458,1460,1464,1467,1475,1477,1501,1503,1505,1512,1513,1516,1539,
%U 1540,1541,1553,1558,1559,1568,1577,1578,1586,1588,1591,1592,1594,1595,1596,1600,1608
%N Numbers that are the sum of eight cubes in exactly ten ways.
%C Differs from A345540 at term 3 because 1262 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 + 5^3 + 10^3 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 6^3 + 10^3 = 1^3 + 1^3 + 1^3 + 4^3 + 5^3 + 5^3 + 6^3 + 9^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 7^3 + 7^3 + 8^3 = 1^3 + 1^3 + 2^3 + 3^3 + 4^3 + 6^3 + 6^3 + 9^3 = 1^3 + 3^3 + 3^3 + 6^3 + 6^3 + 6^3 + 6^3 + 7^3 = 1^3 + 4^3 + 4^3 + 4^3 + 5^3 + 6^3 + 6^3 + 8^3 = 2^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 10^3 = 2^3 + 2^3 + 4^3 + 4^3 + 6^3 + 6^3 + 7^3 + 7^3 = 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 7^3 + 7^3 + 7^3 = 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 5^3 + 9^3.
%C Likely finite.
%H Sean A. Irvine, <a href="/A345792/b345792.txt">Table of n, a(n) for n = 1..161</a>
%e 1243 is a term because 1243 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 5^3 + 9^3 = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 4^3 + 7^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 6^3 + 6^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 5^3 + 5^3 + 8^3 = 1^3 + 1^3 + 4^3 + 4^3 + 5^3 + 5^3 + 5^3 + 6^3 = 1^3 + 2^3 + 3^3 + 5^3 + 5^3 + 5^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 9^3 = 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 6^3 + 6^3 + 6^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 8^3 = 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 6^3 + 7^3.
%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, 8):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 10])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345540, A345782, A345791, A345802, A345842.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 26 2021
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