%I #6 Jul 31 2021 17:58:07

%S 16691,17347,17971,19491,20706,21252,21267,21332,21507,21636,21876,

%T 21956,22547,22612,23156,23587,23652,23827,23892,24436,25107,25347,

%U 25427,25716,25971,26051,27812,29092,29187,29332,29427,29442,29636,29701,29716,29956,29971

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

%H Sean A. Irvine, <a href="/A345573/b345573.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 7):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 7])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A345525, A345564, A345572, A345574, A345582, A345629, A345829.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021