cp's OEIS Frontend

A345851 Numbers that are the sum of nine fourth powers in exactly nine ways.

%I A345851 #6 Jul 31 2021 21:28:38
%S A345851 8259,9539,10709,10819,10884,10949,10964,11124,11444,11573,11668,
%T A345851 11684,11924,12099,12164,12339,12404,12549,12773,12853,12918,13013,
%U A345851 13139,13204,13284,13379,13444,13509,13958,13988,14053,14213,14293,14308,14373,14403,14484
%N A345851 Numbers that are the sum of nine fourth powers in exactly nine ways.
%C A345851 Differs from A345593 at term 2 because 9299 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 8^4  = 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 9^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 7^4 + 8^4  = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4  = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 7^4  = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4  = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 9^4  = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.
%H A345851 Sean A. Irvine, <a href="/A345851/b345851.txt">Table of n, a(n) for n = 1..10000</a>
%e A345851 9299 is a term because 9299 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 7^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 7^4 = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 9^4 = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.
%o A345851 (Python)
%o A345851 from itertools import combinations_with_replacement as cwr
%o A345851 from collections import defaultdict
%o A345851 keep = defaultdict(lambda: 0)
%o A345851 power_terms = [x**4 for x in range(1, 1000)]
%o A345851 for pos in cwr(power_terms, 9):
%o A345851     tot = sum(pos)
%o A345851     keep[tot] += 1
%o A345851     rets = sorted([k for k, v in keep.items() if v == 9])
%o A345851     for x in range(len(rets)):
%o A345851         print(rets[x])
%Y A345851 Cf. A345593, A345801, A345841, A345850, A345852, A345861, A346344.
%K A345851 nonn
%O A345851 1,1
%A A345851 _David Consiglio, Jr._, Jun 26 2021