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A345602 Numbers that are the sum of ten fourth powers in nine or more ways.

%I A345602 #6 Jul 31 2021 17:26:11
%S A345602 6820,6870,6885,6950,7060,7110,7125,7285,7350,7860,7925,7990,8020,
%T A345602 8035,8100,8165,8230,8245,8260,8275,8325,8340,8390,8405,8515,8565,
%U A345602 8580,8645,8755,8820,8884,8965,8995,9030,9045,9060,9075,9125,9140,9205,9220,9235,9270
%N A345602 Numbers that are the sum of ten fourth powers in nine or more ways.
%H A345602 Sean A. Irvine, <a href="/A345602/b345602.txt">Table of n, a(n) for n = 1..10000</a>
%e A345602 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 A345602 (Python)
%o A345602 from itertools import combinations_with_replacement as cwr
%o A345602 from collections import defaultdict
%o A345602 keep = defaultdict(lambda: 0)
%o A345602 power_terms = [x**4 for x in range(1, 1000)]
%o A345602 for pos in cwr(power_terms, 10):
%o A345602     tot = sum(pos)
%o A345602     keep[tot] += 1
%o A345602     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345602     for x in range(len(rets)):
%o A345602         print(rets[x])
%Y A345602 Cf. A345557, A345593, A345601, A345603, A345641, A345861.
%K A345602 nonn
%O A345602 1,1
%A A345602 _David Consiglio, Jr._, Jun 20 2021