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A345792 Numbers that are the sum of eight cubes in exactly ten ways.

%I A345792 #6 Jul 31 2021 22:37:34
%S A345792 1185,1243,1288,1295,1299,1386,1397,1400,1412,1423,1448,1449,1451,
%T A345792 1458,1460,1464,1467,1475,1477,1501,1503,1505,1512,1513,1516,1539,
%U A345792 1540,1541,1553,1558,1559,1568,1577,1578,1586,1588,1591,1592,1594,1595,1596,1600,1608
%N A345792 Numbers that are the sum of eight cubes in exactly ten ways.
%C A345792 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 A345792 Likely finite.
%H A345792 Sean A. Irvine, <a href="/A345792/b345792.txt">Table of n, a(n) for n = 1..161</a>
%e A345792 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 A345792 (Python)
%o A345792 from itertools import combinations_with_replacement as cwr
%o A345792 from collections import defaultdict
%o A345792 keep = defaultdict(lambda: 0)
%o A345792 power_terms = [x**3 for x in range(1, 1000)]
%o A345792 for pos in cwr(power_terms, 8):
%o A345792     tot = sum(pos)
%o A345792     keep[tot] += 1
%o A345792     rets = sorted([k for k, v in keep.items() if v == 10])
%o A345792     for x in range(len(rets)):
%o A345792         print(rets[x])
%Y A345792 Cf. A345540, A345782, A345791, A345802, A345842.
%K A345792 nonn
%O A345792 1,1
%A A345792 _David Consiglio, Jr._, Jun 26 2021