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A345773 Numbers that are the sum of seven cubes in exactly one way.

%I A345773 #8 Jul 31 2021 22:39:08
%S A345773 7,14,21,28,33,35,40,42,47,49,54,56,59,61,66,68,70,73,75,77,80,84,85,
%T A345773 87,91,92,94,96,98,99,103,105,106,110,111,112,113,117,118,122,124,125,
%U A345773 129,132,133,136,137,138,140,143,144,145,147,148,150,151,152,154
%N A345773 Numbers that are the sum of seven cubes in exactly one way.
%C A345773 Differs from A003330 at term 44 because 131 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.
%C A345773 Likely finite.
%H A345773 Sean A. Irvine, <a href="/A345773/b345773.txt">Table of n, a(n) for n = 1..324</a>
%e A345773 14 is a term because 14 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3.
%o A345773 (Python)
%o A345773 from itertools import combinations_with_replacement as cwr
%o A345773 from collections import defaultdict
%o A345773 keep = defaultdict(lambda: 0)
%o A345773 power_terms = [x**3 for x in range(1, 1000)]
%o A345773 for pos in cwr(power_terms, 7):
%o A345773     tot = sum(pos)
%o A345773     keep[tot] += 1
%o A345773     rets = sorted([k for k, v in keep.items() if v == 1])
%o A345773     for x in range(len(rets)):
%o A345773         print(rets[x])
%Y A345773 Cf. A003330, A048929, A345774, A345783, A345823.
%K A345773 nonn
%O A345773 1,1
%A A345773 _David Consiglio, Jr._, Jun 26 2021