A345783 - OEIS

%I #7 Jul 31 2021 22:37:04

%S 8,15,22,29,34,36,41,43,48,50,55,57,60,62,64,67,69,71,74,76,78,81,83,

%T 85,86,88,92,93,95,97,99,100,102,104,106,107,111,112,113,114,118,119,

%U 120,121,123,125,126,130,133,134,137,138,140,141,144,145,146,148

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

%C Differs from A003331 at term 49 because 132 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.

%C Likely finite.

%H Sean A. Irvine, <a href="/A345783/b345783.txt">Table of n, a(n) for n = 1..209</a>

%e 15 is a term because 15 = 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, 8):

%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. A003331, A345773, A345784, A345793, A345833.

%K nonn

%O 1,1

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