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A345794 Numbers that are the sum of nine cubes in exactly two ways.

%I A345794 #6 Jul 31 2021 22:32:38
%S A345794 72,133,140,147,159,161,166,168,175,182,185,187,189,194,196,198,201,
%T A345794 203,205,208,213,217,220,222,227,239,243,246,252,261,265,266,273,289,
%U A345794 296,304,306,308,323,325,328,329,330,336,342,344,349,351,352,354,356,358
%N A345794 Numbers that are the sum of nine cubes in exactly two ways.
%C A345794 Differs from A345541 at term 25 because 224 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3  = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3  = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3  = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.
%C A345794 Likely finite.
%H A345794 Sean A. Irvine, <a href="/A345794/b345794.txt">Table of n, a(n) for n = 1..105</a>
%e A345794 133 is a term because 133 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3.
%o A345794 (Python)
%o A345794 from itertools import combinations_with_replacement as cwr
%o A345794 from collections import defaultdict
%o A345794 keep = defaultdict(lambda: 0)
%o A345794 power_terms = [x**3 for x in range(1, 1000)]
%o A345794 for pos in cwr(power_terms, 9):
%o A345794     tot = sum(pos)
%o A345794     keep[tot] += 1
%o A345794     rets = sorted([k for k, v in keep.items() if v == 2])
%o A345794     for x in range(len(rets)):
%o A345794         print(rets[x])
%Y A345794 Cf. A345541, A345784, A345793, A345795, A345804, A345844.
%K A345794 nonn
%O A345794 1,1
%A A345794 _David Consiglio, Jr._, Jun 26 2021