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A345774 Numbers that are the sum of seven cubes in exactly two ways.

%I A345774 #6 Jul 31 2021 22:39:11
%S A345774 131,159,166,173,185,192,211,236,243,257,264,269,274,276,288,290,292,
%T A345774 295,299,300,302,307,309,311,314,320,321,325,332,333,337,339,340,344,
%U A345774 348,351,353,355,358,359,360,363,372,384,385,386,388,389,393,395,398,403
%N A345774 Numbers that are the sum of seven cubes in exactly two ways.
%C A345774 Differs from A345520 at term 8 because 222 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3  = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3  = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3.
%C A345774 Likely finite.
%H A345774 Sean A. Irvine, <a href="/A345774/b345774.txt">Table of n, a(n) for n = 1..355</a>
%e A345774 159 is a term because 159 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3.
%o A345774 (Python)
%o A345774 from itertools import combinations_with_replacement as cwr
%o A345774 from collections import defaultdict
%o A345774 keep = defaultdict(lambda: 0)
%o A345774 power_terms = [x**3 for x in range(1, 1000)]
%o A345774 for pos in cwr(power_terms, 7):
%o A345774     tot = sum(pos)
%o A345774     keep[tot] += 1
%o A345774     rets = sorted([k for k, v in keep.items() if v == 2])
%o A345774     for x in range(len(rets)):
%o A345774         print(rets[x])
%Y A345774 Cf. A048930, A345520, A345773, A345775, A345784, A345824.
%K A345774 nonn
%O A345774 1,1
%A A345774 _David Consiglio, Jr._, Jun 26 2021