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A345804 Numbers that are the sum of ten cubes in exactly two ways.

%I A345804 #6 Jul 31 2021 22:27:12
%S A345804 73,80,99,134,136,141,148,155,160,162,167,169,174,176,183,186,188,190,
%T A345804 192,193,195,199,202,204,206,209,211,212,213,214,216,218,221,223,228,
%U A345804 230,235,240,244,247,249,254,262,266,269,270,273,274,290,292,297,304
%N A345804 Numbers that are the sum of ten cubes in exactly two ways.
%C A345804 Differs from A345550 at term 22 because 197 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 5^3  = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3  = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 5^3.
%C A345804 Likely finite.
%H A345804 Sean A. Irvine, <a href="/A345804/b345804.txt">Table of n, a(n) for n = 1..90</a>
%e A345804 80 is a term because 80 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3.
%o A345804 (Python)
%o A345804 from itertools import combinations_with_replacement as cwr
%o A345804 from collections import defaultdict
%o A345804 keep = defaultdict(lambda: 0)
%o A345804 power_terms = [x**3 for x in range(1, 1000)]
%o A345804 for pos in cwr(power_terms, 10):
%o A345804     tot = sum(pos)
%o A345804     keep[tot] += 1
%o A345804     rets = sorted([k for k, v in keep.items() if v == 2])
%o A345804     for x in range(len(rets)):
%o A345804         print(rets[x])
%Y A345804 Cf. A345550, A345794, A345803, A345805, A345854.
%K A345804 nonn
%O A345804 1,1
%A A345804 _David Consiglio, Jr._, Jun 26 2021