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A345507 Numbers that are the sum of six fifth powers in two or more ways.

%I A345507 #6 Jul 31 2021 16:37:17
%S A345507 4098,4129,4340,5121,7222,11873,20904,36865,51447,51478,51509,51689,
%T A345507 51720,51931,52470,52501,52712,53493,54571,54602,54813,55594,57695,
%U A345507 59222,59253,59464,60245,62346,63146,66997,67586,68253,68284,68495,68906,68937,69148,69276
%N A345507 Numbers that are the sum of six fifth powers in two or more ways.
%H A345507 Sean A. Irvine, <a href="/A345507/b345507.txt">Table of n, a(n) for n = 1..10000</a>
%e A345507 4129 is a term because 4129 = 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
%o A345507 (Python)
%o A345507 from itertools import combinations_with_replacement as cwr
%o A345507 from collections import defaultdict
%o A345507 keep = defaultdict(lambda: 0)
%o A345507 power_terms = [x**5 for x in range(1, 1000)]
%o A345507 for pos in cwr(power_terms, 6):
%o A345507     tot = sum(pos)
%o A345507     keep[tot] += 1
%o A345507     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345507     for x in range(len(rets)):
%o A345507         print(rets[x])
%Y A345507 Cf. A003351, A342685, A345559, A345604, A345605, A346357.
%K A345507 nonn
%O A345507 1,1
%A A345507 _David Consiglio, Jr._, Jun 20 2021