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A345570 Numbers that are the sum of seven fourth powers in four or more ways.

%I A345570 #6 Jul 31 2021 17:57:57
%S A345570 2932,4147,4212,4387,5427,5602,5667,6627,6642,6692,6707,6772,6817,
%T A345570 6822,6837,6852,6867,6882,6947,7012,7122,7251,7316,7491,7747,7857,
%U A345570 7922,7987,8052,8097,8162,8227,8402,8467,8532,8707,8787,8962,9027,9092,9157,9172,9202
%N A345570 Numbers that are the sum of seven fourth powers in four or more ways.
%H A345570 Sean A. Irvine, <a href="/A345570/b345570.txt">Table of n, a(n) for n = 1..10000</a>
%e A345570 4147 is a term because 4147 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4.
%o A345570 (Python)
%o A345570 from itertools import combinations_with_replacement as cwr
%o A345570 from collections import defaultdict
%o A345570 keep = defaultdict(lambda: 0)
%o A345570 power_terms = [x**4 for x in range(1, 1000)]
%o A345570 for pos in cwr(power_terms, 7):
%o A345570     tot = sum(pos)
%o A345570     keep[tot] += 1
%o A345570     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345570     for x in range(len(rets)):
%o A345570         print(rets[x])
%Y A345570 Cf. A345522, A345561, A345569, A345571, A345579, A345607, A345826.
%K A345570 nonn
%O A345570 1,1
%A A345570 _David Consiglio, Jr._, Jun 20 2021