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A345718 Numbers that are the sum of six fifth powers in four or more ways.

%I A345718 #7 Jul 31 2021 16:37:31
%S A345718 12047994,20646208,21017489,21300963,21741819,24993485,27669050,
%T A345718 28576064,30193856,30785920,35480456,35735194,36082750,37303264,
%U A345718 39035975,46814942,47963291,50047062,50724345,52987561,53076800,53606848,54827300,55101101,56766906
%N A345718 Numbers that are the sum of six fifth powers in four or more ways.
%H A345718 Sean A. Irvine, <a href="/A345718/b345718.txt">Table of n, a(n) for n = 1..10000</a>
%e A345718 20646208 is a term because 20646208 = 2^5 + 12^5 + 12^5 + 16^5 + 18^5 + 28^5 = 3^5 + 4^5 + 4^5 + 8^5 + 10^5 + 29^5 = 6^5 + 6^5 + 12^5 + 14^5 + 24^5 + 26^5 = 7^5 + 7^5 + 8^5 + 16^5 + 25^5 + 25^5.
%o A345718 (Python)
%o A345718 from itertools import combinations_with_replacement as cwr
%o A345718 from collections import defaultdict
%o A345718 keep = defaultdict(lambda: 0)
%o A345718 power_terms = [x**5 for x in range(1, 1000)]
%o A345718 for pos in cwr(power_terms, 6):
%o A345718     tot = sum(pos)
%o A345718     keep[tot] += 1
%o A345718     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345718     for x in range(len(rets)):
%o A345718         print(rets[x])
%Y A345718 Cf. A344518, A345561, A345604, A345607, A345719, A346359.
%K A345718 nonn
%O A345718 1,1
%A A345718 _David Consiglio, Jr._, Jun 24 2021