A345801 - OEIS

%I #6 Jul 31 2021 22:33:02

%S 859,861,896,903,922,929,935,939,959,973,997,999,1009,1016,1020,1023,

%T 1027,1029,1030,1034,1035,1036,1037,1041,1046,1059,1060,1064,1065,

%U 1066,1067,1071,1072,1079,1086,1091,1105,1116,1131,1138,1146,1152,1155,1157,1158

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

%C Differs from A345548 at term 10 because 966 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 6^3 + 9^3  = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 + 8^3  = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 9^3  = 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 + 5^3 + 6^3 + 7^3  = 1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 + 6^3 + 7^3  = 1^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 8^3  = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3 + 9^3  = 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 5^3 + 5^3 + 6^3 + 7^3  = 2^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 7^3 + 7^3  = 3^3 + 4^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3.

%C Likely finite.

%H Sean A. Irvine, <a href="/A345801/b345801.txt">Table of n, a(n) for n = 1..86</a>

%e 861 is a term because 861 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 8^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 5^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 6^3 = 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 8^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 = 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3.

%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 == 9])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A345548, A345791, A345800, A345802, A345811, A345851.

%K nonn

%O 1,1

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