A345611 - OEIS

%I #6 Jul 31 2021 16:17:02

%S 52417,54518,69634,70954,84458,84489,84700,85481,87582,92233,101264,

%T 102890,112574,117225,119326,134473,143264,143442,143506,149781,

%U 151448,158719,159465,165634,166998,167029,167196,167240,168021,170122,174773,183804,184457

%N Numbers that are the sum of eight fifth powers in three or more ways.

%H Sean A. Irvine, <a href="/A345611/b345611.txt">Table of n, a(n) for n = 1..10000</a>

%e 54518 is a term because 54518 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5 = 1^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 7^5 + 7^5 + 7^5.

%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**5 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 >= 3])

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

%o         print(rets[x])

%Y Cf. A345578, A345606, A345610, A345612, A345620, A346328.

%K nonn

%O 1,1

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