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A345841 Numbers that are the sum of eight fourth powers in exactly nine ways.

%I A345841 #6 Jul 31 2021 21:33:51
%S A345841 15427,16692,17348,17493,18052,18227,19267,19412,19572,19748,20852,
%T A345841 21443,21493,21637,21652,21653,21827,21877,21972,22037,22212,22388,
%U A345841 22501,22548,22868,22932,23107,23412,23413,23428,23828,23893,23972,24037,24131,24212,24517
%N A345841 Numbers that are the sum of eight fourth powers in exactly nine ways.
%C A345841 Differs from A345584 at term 5 because 17972 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 9^4 + 10^4  = 1^4 + 1^4 + 5^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4  = 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 5^4 + 7^4 + 11^4  = 1^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 6^4 + 11^4  = 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 7^4 + 8^4 + 10^4  = 1^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 + 10^4  = 1^4 + 4^4 + 5^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4  = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 8^4 + 9^4 + 9^4  = 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 7^4 + 9^4 + 9^4  = 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 9^4 + 9^4.
%H A345841 Sean A. Irvine, <a href="/A345841/b345841.txt">Table of n, a(n) for n = 1..10000</a>
%e A345841 16692 is a term because 16692 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4 = 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 5^4 + 7^4 + 9^4 + 9^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 9^4 + 9^4.
%o A345841 (Python)
%o A345841 from itertools import combinations_with_replacement as cwr
%o A345841 from collections import defaultdict
%o A345841 keep = defaultdict(lambda: 0)
%o A345841 power_terms = [x**4 for x in range(1, 1000)]
%o A345841 for pos in cwr(power_terms, 8):
%o A345841     tot = sum(pos)
%o A345841     keep[tot] += 1
%o A345841     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345841     for x in range(len(rets)):
%o A345841         print(rets[x])
%Y A345841 Cf. A345584, A345791, A345831, A345840, A345842, A345851, A346334.
%K A345841 nonn
%O A345841 1,1
%A A345841 _David Consiglio, Jr._, Jun 26 2021