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A345592 Numbers that are the sum of nine fourth powers in eight or more ways.

%I A345592 #6 Jul 31 2021 17:39:13
%S A345592 6804,6869,8019,8084,8259,8324,8499,8564,9044,9124,9219,9234,9284,
%T A345592 9299,9364,9429,9474,9494,9539,9604,9669,9749,9779,10148,10259,10293,
%U A345592 10339,10388,10453,10514,10579,10628,10644,10709,10754,10789,10819,10884,10949,10964
%N A345592 Numbers that are the sum of nine fourth powers in eight or more ways.
%H A345592 Sean A. Irvine, <a href="/A345592/b345592.txt">Table of n, a(n) for n = 1..10000</a>
%e A345592 6869 is a term because 6869 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.
%o A345592 (Python)
%o A345592 from itertools import combinations_with_replacement as cwr
%o A345592 from collections import defaultdict
%o A345592 keep = defaultdict(lambda: 0)
%o A345592 power_terms = [x**4 for x in range(1, 1000)]
%o A345592 for pos in cwr(power_terms, 9):
%o A345592     tot = sum(pos)
%o A345592     keep[tot] += 1
%o A345592     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345592     for x in range(len(rets)):
%o A345592         print(rets[x])
%Y A345592 Cf. A345547, A345583, A345591, A345593, A345601, A345625, A345850.
%K A345592 nonn
%O A345592 1,1
%A A345592 _David Consiglio, Jr._, Jun 20 2021