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A345861 Numbers that are the sum of ten fourth powers in exactly nine ways.

%I A345861 #6 Jul 31 2021 20:00:32
%S A345861 6820,6870,6950,7060,7110,7125,7285,7350,7860,7925,8020,8230,8245,
%T A345861 8260,8325,8390,8405,8645,8755,8820,8884,8965,8995,9030,9045,9060,
%U A345861 9075,9125,9220,9270,9365,9430,9475,9490,9525,9605,9730,9735,9765,9815,9895,9910,10035
%N A345861 Numbers that are the sum of ten fourth powers in exactly nine ways.
%C A345861 Differs from A345602 at term 3 because 6885 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4  = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4  = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4  = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4  = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.
%H A345861 Sean A. Irvine, <a href="/A345861/b345861.txt">Table of n, a(n) for n = 1..10000</a>
%e A345861 6870 is a term because 6870 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4 + 7^4.
%o A345861 (Python)
%o A345861 from itertools import combinations_with_replacement as cwr
%o A345861 from collections import defaultdict
%o A345861 keep = defaultdict(lambda: 0)
%o A345861 power_terms = [x**4 for x in range(1, 1000)]
%o A345861 for pos in cwr(power_terms, 10):
%o A345861     tot = sum(pos)
%o A345861     keep[tot] += 1
%o A345861     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345861     for x in range(len(rets)):
%o A345861         print(rets[x])
%Y A345861 Cf. A345602, A345811, A345851, A345860, A345862, A346354.
%K A345861 nonn
%O A345861 1,1
%A A345861 _David Consiglio, Jr._, Jun 26 2021