A345536 - OEIS

%I #6 Aug 05 2021 15:20:56

%S 628,719,769,776,778,795,832,839,846,858,860,865,872,875,876,882,886,

%T 891,893,895,901,902,907,908,912,921,927,928,931,938,945,946,947,951,

%U 954,956,958,963,964,965,970,972,977,982,984,989,991,992,996,998,999,1001

%N Numbers that are the sum of eight cubes in six or more ways.

%H Sean A. Irvine, <a href="/A345536/b345536.txt">Table of n, a(n) for n = 1..10000</a>

%e 719 is a term because 719 = 1^3 + 1^3 + 1^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 2^3 + 3^3 + 4^3 + 4^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 + 5^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 5^3 + 6^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 = 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3.

%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 >= 6])

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

%o         print(rets[x])

%Y Cf. A345493, A345524, A345535, A345537, A345545, A345581, A345788.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021