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%I #6 Jul 31 2021 22:27:09
%S 10,17,24,31,36,38,43,45,50,52,57,59,62,64,66,69,71,76,78,83,85,87,88,
%T 90,92,94,95,97,101,102,104,106,108,109,111,113,114,115,116,118,120,
%U 121,122,123,125,127,128,129,130,132,135,137,139,140,142,143,146
%N Numbers that are the sum of ten cubes in exactly one ways.
%C Differs from A003333 at term 18 because 73 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3.
%C Likely finite.
%H Sean A. Irvine, <a href="/A345803/b345803.txt">Table of n, a(n) for n = 1..151</a>
%e 17 is a term because 17 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**3 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 10):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 1])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A003333, A345793, A345804, A345853.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 26 2021
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