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A345604 Numbers that are the sum of six fifth powers in three or more ways.

%I A345604 #6 Jul 31 2021 16:37:28
%S A345604 696467,893572,1100264,1109295,1165727,1711776,2007401,2025309,
%T A345604 2221767,2801812,3047519,3310494,3360608,3550866,3559556,3576120,
%U A345604 3807122,3907101,4055922,4093540,4096114,4104067,4123363,4135578,4155107,4195571,4222339,4326784,4417112
%N A345604 Numbers that are the sum of six fifth powers in three or more ways.
%H A345604 Sean A. Irvine, <a href="/A345604/b345604.txt">Table of n, a(n) for n = 1..10000</a>
%e A345604 893572 is a term because 893572 = 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 = 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 = 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5.
%o A345604 (Python)
%o A345604 from itertools import combinations_with_replacement as cwr
%o A345604 from collections import defaultdict
%o A345604 keep = defaultdict(lambda: 0)
%o A345604 power_terms = [x**5 for x in range(1, 1000)]
%o A345604 for pos in cwr(power_terms, 6):
%o A345604     tot = sum(pos)
%o A345604     keep[tot] += 1
%o A345604     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345604     for x in range(len(rets)):
%o A345604         print(rets[x])
%Y A345604 Cf. A342687, A345507, A345560, A345606, A345718, A346358.
%K A345604 nonn
%O A345604 1,1
%A A345604 _David Consiglio, Jr._, Jun 20 2021