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A345836 Numbers that are the sum of eight fourth powers in exactly four ways.

%I A345836 #6 Jul 31 2021 21:33:34
%S A345836 2933,2948,3013,3173,3188,3557,4148,4163,4213,4293,4388,4453,4643,
%T A345836 4772,4837,4883,5012,5123,5188,5203,5268,5333,5363,5378,5398,5428,
%U A345836 5538,5573,5603,5618,5668,5733,5748,5858,5923,6052,6163,6227,6292,6548,6578,6628,6693
%N A345836 Numbers that are the sum of eight fourth powers in exactly four ways.
%C A345836 Differs from A345579 at term 10 because 4228 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 8^4  = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 6^4 + 7^4  = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4  = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4  = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4.
%H A345836 Sean A. Irvine, <a href="/A345836/b345836.txt">Table of n, a(n) for n = 1..10000</a>
%e A345836 2948 is a term because 2948 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4.
%o A345836 (Python)
%o A345836 from itertools import combinations_with_replacement as cwr
%o A345836 from collections import defaultdict
%o A345836 keep = defaultdict(lambda: 0)
%o A345836 power_terms = [x**4 for x in range(1, 1000)]
%o A345836 for pos in cwr(power_terms, 8):
%o A345836     tot = sum(pos)
%o A345836     keep[tot] += 1
%o A345836     rets = sorted([k for k, v in keep.items() if v == 4])
%o A345836     for x in range(len(rets)):
%o A345836         print(rets[x])
%Y A345836 Cf. A345579, A345786, A345826, A345835, A345837, A345846, A346329.
%K A345836 nonn
%O A345836 1,1
%A A345836 _David Consiglio, Jr._, Jun 26 2021