cp's OEIS Frontend

A345831 Numbers that are the sum of seven fourth powers in exactly nine ways.

%I A345831 #6 Jul 31 2021 21:37:04
%S A345831 19491,21267,21332,23652,35427,36052,37812,38067,39891,40356,41732,
%T A345831 41747,43267,43876,43891,43956,44131,44196,44532,44612,45156,45171,
%U A345831 45411,45651,45652,45891,46276,46451,46516,47427,48036,48052,48532,48707,49747,49956,49987
%N A345831 Numbers that are the sum of seven fourth powers in exactly nine ways.
%C A345831 Differs from A345575 at term 5 because 31251 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 10^4 + 12^4  = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 10^4 + 11^4  = 1^4 + 4^4 + 4^4 + 4^4 + 5^4 + 6^4 + 13^4  = 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 + 10^4  = 2^4 + 2^4 + 2^4 + 5^4 + 6^4 + 11^4 + 11^4  = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 10^4 + 11^4  = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 10^4 + 12^4  = 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 + 10^4  = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 + 11^4  = 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 + 11^4.
%H A345831 Sean A. Irvine, <a href="/A345831/b345831.txt">Table of n, a(n) for n = 1..10000</a>
%e A345831 21267 is a term because 21267 = 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 12^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4 = 1^4 + 2^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4 = 2^4 + 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 11^4 = 3^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 + 8^4.
%o A345831 (Python)
%o A345831 from itertools import combinations_with_replacement as cwr
%o A345831 from collections import defaultdict
%o A345831 keep = defaultdict(lambda: 0)
%o A345831 power_terms = [x**4 for x in range(1, 1000)]
%o A345831 for pos in cwr(power_terms, 7):
%o A345831     tot = sum(pos)
%o A345831     keep[tot] += 1
%o A345831     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345831     for x in range(len(rets)):
%o A345831         print(rets[x])
%Y A345831 Cf. A345575, A345781, A345821, A345830, A345832, A345841, A346286.
%K A345831 nonn
%O A345831 1,1
%A A345831 _David Consiglio, Jr._, Jun 26 2021