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A345610 Numbers that are the sum of eight fifth powers in two or more ways.

%I A345610 #6 Jul 31 2021 16:16:56
%S A345610 4100,4131,4162,4193,4342,4373,4404,4584,4615,4826,5123,5154,5185,
%T A345610 5365,5396,5607,6146,6177,6388,7169,7224,7255,7286,7466,7497,7708,
%U A345610 8247,8278,8489,9270,10348,10379,10590,11371,11875,11906,11937,12117,12148,12359,12898
%N A345610 Numbers that are the sum of eight fifth powers in two or more ways.
%H A345610 Sean A. Irvine, <a href="/A345610/b345610.txt">Table of n, a(n) for n = 1..10000</a>
%e A345610 4131 is a term because 4131 = 1^5 + 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
%o A345610 (Python)
%o A345610 from itertools import combinations_with_replacement as cwr
%o A345610 from collections import defaultdict
%o A345610 keep = defaultdict(lambda: 0)
%o A345610 power_terms = [x**5 for x in range(1, 1000)]
%o A345610 for pos in cwr(power_terms, 8):
%o A345610     tot = sum(pos)
%o A345610     keep[tot] += 1
%o A345610     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345610     for x in range(len(rets)):
%o A345610         print(rets[x])
%Y A345610 Cf. A003353, A345577, A345605, A345611, A345619, A346327.
%K A345610 nonn
%O A345610 1,1
%A A345610 _David Consiglio, Jr._, Jun 20 2021