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A345573 Numbers that are the sum of seven fourth powers in seven or more ways.

%I A345573 #6 Jul 31 2021 17:58:07
%S A345573 16691,17347,17971,19491,20706,21252,21267,21332,21507,21636,21876,
%T A345573 21956,22547,22612,23156,23587,23652,23827,23892,24436,25107,25347,
%U A345573 25427,25716,25971,26051,27812,29092,29187,29332,29427,29442,29636,29701,29716,29956,29971
%N A345573 Numbers that are the sum of seven fourth powers in seven or more ways.
%H A345573 Sean A. Irvine, <a href="/A345573/b345573.txt">Table of n, a(n) for n = 1..10000</a>
%e A345573 17347 is a term because 17347 = 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4 + 9^4 + 9^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 9^4 + 9^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 9^4 + 9^4.
%o A345573 (Python)
%o A345573 from itertools import combinations_with_replacement as cwr
%o A345573 from collections import defaultdict
%o A345573 keep = defaultdict(lambda: 0)
%o A345573 power_terms = [x**4 for x in range(1, 1000)]
%o A345573 for pos in cwr(power_terms, 7):
%o A345573     tot = sum(pos)
%o A345573     keep[tot] += 1
%o A345573     rets = sorted([k for k, v in keep.items() if v >= 7])
%o A345573     for x in range(len(rets)):
%o A345573         print(rets[x])
%Y A345573 Cf. A345525, A345564, A345572, A345574, A345582, A345629, A345829.
%K A345573 nonn
%O A345573 1,1
%A A345573 _David Consiglio, Jr._, Jun 20 2021