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A345569 Numbers that are the sum of seven fourth powers in three or more ways.

%I A345569 #6 Jul 31 2021 17:57:54
%S A345569 2677,2692,2757,2852,2867,2917,2932,2997,3107,3172,3301,3476,3541,
%T A345569 3972,4132,4147,4212,4227,4242,4257,4307,4322,4372,4387,4437,4452,
%U A345569 4482,4497,4562,4627,4737,4756,4851,4866,4867,4931,4996,5077,5106,5107,5122,5187,5252
%N A345569 Numbers that are the sum of seven fourth powers in three or more ways.
%H A345569 Sean A. Irvine, <a href="/A345569/b345569.txt">Table of n, a(n) for n = 1..10000</a>
%e A345569 2692 is a term because 2692 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.
%o A345569 (Python)
%o A345569 from itertools import combinations_with_replacement as cwr
%o A345569 from collections import defaultdict
%o A345569 keep = defaultdict(lambda: 0)
%o A345569 power_terms = [x**4 for x in range(1, 1000)]
%o A345569 for pos in cwr(power_terms, 7):
%o A345569     tot = sum(pos)
%o A345569     keep[tot] += 1
%o A345569     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345569     for x in range(len(rets)):
%o A345569         print(rets[x])
%Y A345569 Cf. A345521, A345560, A345568, A345570, A345578, A345606, A345825.
%K A345569 nonn
%O A345569 1,1
%A A345569 _David Consiglio, Jr._, Jun 20 2021