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A345601 Numbers that are the sum of ten fourth powers in eight or more ways.

%I A345601 #6 Jul 31 2021 17:26:02
%S A345601 6675,6740,6755,6805,6820,6870,6885,6950,6995,7015,7030,7045,7060,
%T A345601 7095,7110,7125,7270,7285,7300,7350,7365,7429,7494,7525,7540,7590,
%U A345601 7605,7750,7780,7845,7860,7925,7955,7990,8005,8020,8035,8085,8100,8150,8165,8195,8215
%N A345601 Numbers that are the sum of ten fourth powers in eight or more ways.
%H A345601 Sean A. Irvine, <a href="/A345601/b345601.txt">Table of n, a(n) for n = 1..10000</a>
%e A345601 6740 is a term because 6740 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 = 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 8^4.
%o A345601 (Python)
%o A345601 from itertools import combinations_with_replacement as cwr
%o A345601 from collections import defaultdict
%o A345601 keep = defaultdict(lambda: 0)
%o A345601 power_terms = [x**4 for x in range(1, 1000)]
%o A345601 for pos in cwr(power_terms, 10):
%o A345601     tot = sum(pos)
%o A345601     keep[tot] += 1
%o A345601     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345601     for x in range(len(rets)):
%o A345601         print(rets[x])
%Y A345601 Cf. A345556, A345592, A345600, A345602, A345640, A345860.
%K A345601 nonn
%O A345601 1,1
%A A345601 _David Consiglio, Jr._, Jun 20 2021