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A345814 Numbers that are the sum of six fourth powers in exactly two ways.

%I A345814 #6 Jul 31 2021 21:57:13
%S A345814 261,276,291,341,356,421,516,531,596,771,885,900,965,1140,1361,1509,
%T A345814 1556,1571,1636,1811,2180,2596,2611,2661,2691,2706,2721,2741,2756,
%U A345814 2771,2786,2836,2931,2946,2961,3011,3026,3091,3186,3201,3220,3266,3285,3300,3315
%N A345814 Numbers that are the sum of six fourth powers in exactly two ways.
%C A345814 Differs from A345559 at term 25 because 2676 = 1^4 + 1^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.
%H A345814 Sean A. Irvine, <a href="/A345814/b345814.txt">Table of n, a(n) for n = 1..10000</a>
%e A345814 276 is a term because 276 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.
%o A345814 (Python)
%o A345814 from itertools import combinations_with_replacement as cwr
%o A345814 from collections import defaultdict
%o A345814 keep = defaultdict(lambda: 0)
%o A345814 power_terms = [x**4 for x in range(1, 1000)]
%o A345814 for pos in cwr(power_terms, 6):
%o A345814     tot = sum(pos)
%o A345814     keep[tot] += 1
%o A345814     rets = sorted([k for k, v in keep.items() if v == 2])
%o A345814     for x in range(len(rets)):
%o A345814         print(rets[x])
%Y A345814 Cf. A048930, A344237, A345559, A345813, A345815, A345824, A346357.
%K A345814 nonn
%O A345814 1,1
%A A345814 _David Consiglio, Jr._, Jun 26 2021