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A345849 Numbers that are the sum of nine fourth powers in exactly seven ways.

%I A345849 #6 Jul 31 2021 21:28:31
%S A345849 6739,6854,6979,7029,7044,7094,7109,7269,7284,7844,7909,7939,8004,
%T A345849 8149,8194,8244,8309,8389,8434,8628,8739,8868,8979,9059,9189,9254,
%U A345849 9414,9509,9524,9668,9684,9734,9814,9829,9843,9844,9908,9909,9924,9989,10019,10038,10084
%N A345849 Numbers that are the sum of nine fourth powers in exactly seven ways.
%C A345849 Differs from A345591 at term 2 because 6804 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 8^4  = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 8^4  = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4  = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.
%H A345849 Sean A. Irvine, <a href="/A345849/b345849.txt">Table of n, a(n) for n = 1..10000</a>
%e A345849 6804 is a term because 6804 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.
%o A345849 (Python)
%o A345849 from itertools import combinations_with_replacement as cwr
%o A345849 from collections import defaultdict
%o A345849 keep = defaultdict(lambda: 0)
%o A345849 power_terms = [x**4 for x in range(1, 1000)]
%o A345849 for pos in cwr(power_terms, 9):
%o A345849     tot = sum(pos)
%o A345849     keep[tot] += 1
%o A345849     rets = sorted([k for k, v in keep.items() if v == 7])
%o A345849     for x in range(len(rets)):
%o A345849         print(rets[x])
%Y A345849 Cf. A345591, A345799, A345839, A345848, A345850, A345859, A346342.
%K A345849 nonn
%O A345849 1,1
%A A345849 _David Consiglio, Jr._, Jun 26 2021