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A345859 Numbers that are the sum of ten fourth powers in exactly seven ways.

%I A345859 #6 Jul 31 2021 20:00:24
%S A345859 4485,5445,5460,5525,5540,5590,5605,5670,5700,5715,5765,5780,5830,
%T A345859 5845,6645,6710,6775,6855,6900,6915,6930,6935,6965,6980,7175,7190,
%U A345859 7235,7255,7335,7364,7415,7430,7475,7479,7495,7510,7604,7620,7654,7669,7670,7685,7715
%N A345859 Numbers that are the sum of ten fourth powers in exactly seven ways.
%C A345859 Differs from A345600 at term 16 because 6675 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 8^4  = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 9^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4  = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 8^4  = 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4.
%H A345859 Sean A. Irvine, <a href="/A345859/b345859.txt">Table of n, a(n) for n = 1..9598</a>
%e A345859 5445 is a term because 5445 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 7^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 = 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 = 4^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4.
%o A345859 (Python)
%o A345859 from itertools import combinations_with_replacement as cwr
%o A345859 from collections import defaultdict
%o A345859 keep = defaultdict(lambda: 0)
%o A345859 power_terms = [x**4 for x in range(1, 1000)]
%o A345859 for pos in cwr(power_terms, 10):
%o A345859     tot = sum(pos)
%o A345859     keep[tot] += 1
%o A345859     rets = sorted([k for k, v in keep.items() if v == 7])
%o A345859     for x in range(len(rets)):
%o A345859         print(rets[x])
%Y A345859 Cf. A345600, A345809, A345849, A345858, A345860, A346352.
%K A345859 nonn
%O A345859 1,1
%A A345859 _David Consiglio, Jr._, Jun 26 2021