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A345821 Numbers that are the sum of six fourth powers in exactly nine ways.

%I A345821 #6 Jul 31 2021 21:57:36
%S A345821 88595,132546,134931,144835,146450,162355,170275,171555,171795,172036,
%T A345821 172835,177380,177716,180770,183540,184835,185555,187700,187715,
%U A345821 190100,190211,193635,195380,195780,196435,197780,199075,199475,199730,199955,202196,202980
%N A345821 Numbers that are the sum of six fourth powers in exactly nine ways.
%C A345821 Differs from A345566 at term 2 because 122915 = 1^4 + 3^4 + 6^4 + 9^4 + 10^4 + 18^4  = 1^4 + 4^4 + 7^4 + 8^4 + 15^4 + 16^4  = 1^4 + 7^4 + 9^4 + 10^4 + 14^4 + 16^4  = 2^4 + 3^4 + 4^4 + 5^4 + 14^4 + 17^4  = 2^4 + 4^4 + 5^4 + 7^4 + 11^4 + 18^4  = 2^4 + 9^4 + 9^4 + 12^4 + 14^4 + 15^4  = 3^4 + 5^4 + 6^4 + 6^4 + 11^4 + 18^4  = 3^4 + 8^4 + 10^4 + 11^4 + 13^4 + 16^4  = 5^4 + 6^4 + 7^4 + 11^4 + 14^4 + 16^4  = 8^4 + 8^4 + 9^4 + 10^4 + 11^4 + 17^4.
%H A345821 Sean A. Irvine, <a href="/A345821/b345821.txt">Table of n, a(n) for n = 1..10000</a>
%e A345821 122915 is a term because 122915 = 1^4 + 3^4 + 6^4 + 9^4 + 10^4 + 18^4 = 1^4 + 4^4 + 7^4 + 8^4 + 15^4 + 16^4 = 1^4 + 7^4 + 9^4 + 10^4 + 14^4 + 16^4 = 2^4 + 3^4 + 4^4 + 5^4 + 14^4 + 17^4 = 2^4 + 4^4 + 5^4 + 7^4 + 11^4 + 18^4 = 2^4 + 9^4 + 9^4 + 12^4 + 14^4 + 15^4 = 3^4 + 5^4 + 6^4 + 6^4 + 11^4 + 18^4 = 3^4 + 8^4 + 10^4 + 11^4 + 13^4 + 16^4 = 5^4 + 6^4 + 7^4 + 11^4 + 14^4 + 16^4 = 8^4 + 8^4 + 9^4 + 10^4 + 11^4 + 17^4.
%o A345821 (Python)
%o A345821 from itertools import combinations_with_replacement as cwr
%o A345821 from collections import defaultdict
%o A345821 keep = defaultdict(lambda: 0)
%o A345821 power_terms = [x**4 for x in range(1, 1000)]
%o A345821 for pos in cwr(power_terms, 6):
%o A345821     tot = sum(pos)
%o A345821     keep[tot] += 1
%o A345821     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345821     for x in range(len(rets)):
%o A345821         print(rets[x])
%Y A345821 Cf. A341892, A345566, A345771, A345820, A345822, A345831, A346364.
%K A345821 nonn
%O A345821 1,1
%A A345821 _David Consiglio, Jr._, Jun 26 2021