A345184 - OEIS

%I #6 Jul 31 2021 23:16:49

%S 4392,4915,5139,5256,5321,5624,5643,5678,5741,5769,5797,5832,5914,

%T 6075,6202,6499,6560,6616,6642,6677,6833,6884,7008,7111,7128,7155,

%U 7218,7344,7395,7641,7696,7729,7785,7813,7820,7849,7883,8037,8100,8243,8282,8308,8315

%N Numbers that are the sum of five third powers in exactly eight ways.

%C Differs from A345183 at term 13 because 5860  = 1^3 + 1^3 + 5^3 + 8^3 + 16^3  = 1^3 + 2^3 + 3^3 + 11^3 + 15^3  = 1^3 + 3^3 + 8^3 + 11^3 + 14^3  = 1^3 + 5^3 + 5^3 + 10^3 + 15^3  = 1^3 + 9^3 + 10^3 + 10^3 + 12^3  = 2^3 + 3^3 + 8^3 + 9^3 + 15^3  = 2^3 + 3^3 + 5^3 + 12^3 + 14^3  = 2^3 + 8^3 + 8^3 + 12^3 + 12^3  = 3^3 + 8^3 + 8^3 + 9^3 + 14^3  = 3^3 + 6^3 + 7^3 + 12^3 + 13^3.

%H David Consiglio, Jr., <a href="/A345184/b345184.txt">Table of n, a(n) for n = 1..10000</a>

%e 4915 is a term because 4915 = 1^3 + 2^3 + 7^3 + 12^3 + 12^3  = 1^3 + 3^3 + 7^3 + 9^3 + 14^3  = 1^3 + 8^3 + 8^3 + 11^3 + 11^3  = 2^3 + 4^3 + 6^3 + 6^3 + 15^3  = 3^3 + 3^3 + 5^3 + 7^3 + 15^3  = 3^3 + 3^3 + 10^3 + 11^3 + 11^3  = 4^3 + 6^3 + 6^3 + 8^3 + 14^3  = 8^3 + 8^3 + 8^3 + 9^3 + 11^3.

%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, 5):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 8])

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

%o     print(rets[x])

%Y Cf. A294742, A344945, A345153, A345181, A345183, A345186, A345770.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 10 2021