%I #10 Jul 31 2021 22:32:35

%S 9,16,23,30,35,37,42,44,49,51,56,58,61,63,65,68,70,75,77,79,82,84,86,

%T 87,89,91,93,94,96,98,100,101,103,105,107,108,110,112,113,114,115,119,

%U 120,121,122,124,126,127,128,129,131,134,135,138,139,141,142,145

%N Numbers that are the sum of nine cubes in exactly one way.

%C Differs from A003332 at term 18 because 72 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^2 + 1^3 + 4^3 = 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="/A345793/b345793.txt">Table of n, a(n) for n = 1..176</a>

%e 16 is a term because 16 = 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, 9):

%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. A003332, A345783, A345794, A345803, A345843.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021