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A346359 Numbers that are the sum of six fifth powers in exactly four ways.

%I A346359 #6 Jul 31 2021 19:24:17
%S A346359 12047994,20646208,21017489,21300963,21741819,24993485,27669050,
%T A346359 28576064,30193856,30785920,35480456,35735194,36082750,37303264,
%U A346359 39035975,46814942,47963291,50047062,50724345,52987561,53076800,53606848,55101101,56766906,57969327,58125980
%N A346359 Numbers that are the sum of six fifth powers in exactly four ways.
%C A346359 Differs from A345718 at term 23 because 54827300 = 4^5 + 7^5 + 21^5 + 22^5 + 23^5 + 33^5 = 5^5 + 10^5 + 15^5 + 20^5 + 28^5 + 32^5 = 1^5 + 14^5 + 16^5 + 19^5 + 28^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 29^5 + 31^5 = 5^5 + 6^5 + 19^5 + 20^5 + 29^5 + 31^5.
%H A346359 Sean A. Irvine, <a href="/A346359/b346359.txt">Table of n, a(n) for n = 1..10000</a>
%e A346359 12047994 is a term 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.
%o A346359 (Python)
%o A346359 from itertools import combinations_with_replacement as cwr
%o A346359 from collections import defaultdict
%o A346359 keep = defaultdict(lambda: 0)
%o A346359 power_terms = [x**5 for x in range(1, 1000)]
%o A346359 for pos in cwr(power_terms, 6):
%o A346359     tot = sum(pos)
%o A346359     keep[tot] += 1
%o A346359     rets = sorted([k for k, v in keep.items() if v == 4])
%o A346359     for x in range(len(rets)):
%o A346359         print(rets[x])
%Y A346359 Cf. A344519, A345718, A345816, A346281, A346358, A346360.
%K A346359 nonn
%O A346359 1,1
%A A346359 _David Consiglio, Jr._, Jul 13 2021