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A346358 Numbers that are the sum of six fifth powers in exactly three ways.

%I A346358 #6 Jul 31 2021 19:24:13
%S A346358 696467,893572,1100264,1109295,1165727,1711776,2007401,2025309,
%T A346358 2221767,2801812,3047519,3310494,3360608,3550866,3559556,3576120,
%U A346358 3807122,3907101,4055922,4093540,4096114,4104067,4123363,4135578,4155107,4195571,4222339,4326784,4417112
%N A346358 Numbers that are the sum of six fifth powers in exactly three ways.
%C A346358 Differs from A345604 at term 105 because 12047994 = 7^5 + 9^5 + 12^5 + 14^5 + 17^5 + 25^5 = 5^5 + 10^5 + 13^5 + 15^5 + 16^5 + 25^5 = 1^5 + 1^5 + 3^5 + 4^5 + 21^5 + 24^5 = 4^5 + 6^5 + 15^5 + 15^5 + 21^5 + 23^5.
%H A346358 Sean A. Irvine, <a href="/A346358/b346358.txt">Table of n, a(n) for n = 1..10000</a>
%e A346358 696467 is a term because 696467 = 1^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 13^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 13^5.
%o A346358 (Python)
%o A346358 from itertools import combinations_with_replacement as cwr
%o A346358 from collections import defaultdict
%o A346358 keep = defaultdict(lambda: 0)
%o A346358 power_terms = [x**5 for x in range(1, 1000)]
%o A346358 for pos in cwr(power_terms, 6):
%o A346358     tot = sum(pos)
%o A346358     keep[tot] += 1
%o A346358     rets = sorted([k for k, v in keep.items() if v == 3])
%o A346358     for x in range(len(rets)):
%o A346358         print(rets[x])
%Y A346358 Cf. A342688, A345604, A345815, A346280, A346357, A346359.
%K A346358 nonn
%O A346358 1,1
%A A346358 _David Consiglio, Jr._, Jul 13 2021