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A346357 Numbers that are the sum of six fifth powers in exactly two ways.

%I A346357 #6 Jul 31 2021 19:24:09
%S A346357 4098,4129,4340,5121,7222,11873,20904,36865,51447,51478,51509,51689,
%T A346357 51720,51931,52470,52501,52712,53493,54571,54602,54813,55594,57695,
%U A346357 59222,59253,59464,60245,62346,63146,66997,67586,68253,68284,68495,68906,68937,69148,69276
%N A346357 Numbers that are the sum of six fifth powers in exactly two ways.
%C A346357 Differs from A345507 at term 231 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.
%H A346357 Sean A. Irvine, <a href="/A346357/b346357.txt">Table of n, a(n) for n = 1..10000</a>
%e A346357 4098 is a term because 4098 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.
%o A346357 (Python)
%o A346357 from itertools import combinations_with_replacement as cwr
%o A346357 from collections import defaultdict
%o A346357 keep = defaultdict(lambda: 0)
%o A346357 power_terms = [x**5 for x in range(1, 1000)]
%o A346357 for pos in cwr(power_terms, 6):
%o A346357     tot = sum(pos)
%o A346357     keep[tot] += 1
%o A346357     rets = sorted([k for k, v in keep.items() if v == 2])
%o A346357     for x in range(len(rets)):
%o A346357         print(rets[x])
%Y A346357 Cf. A342686, A345507, A345814, A346279, A346356, A346358.
%K A346357 nonn
%O A346357 1,1
%A A346357 _David Consiglio, Jr._, Jul 13 2021