cp's OEIS Frontend

A345593 Numbers that are the sum of nine fourth powers in nine or more ways.

%I A345593 #6 Jul 31 2021 17:39:18
%S A345593 8259,9299,9539,10709,10819,10884,10949,10964,11124,11444,11573,11668,
%T A345593 11684,11924,12099,12164,12339,12404,12549,12708,12773,12853,12918,
%U A345593 12948,13013,13139,13204,13269,13284,13349,13379,13444,13509,13524,13589,13764,13829
%N A345593 Numbers that are the sum of nine fourth powers in nine or more ways.
%H A345593 Sean A. Irvine, <a href="/A345593/b345593.txt">Table of n, a(n) for n = 1..10000</a>
%e A345593 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 A345593 (Python)
%o A345593 from itertools import combinations_with_replacement as cwr
%o A345593 from collections import defaultdict
%o A345593 keep = defaultdict(lambda: 0)
%o A345593 power_terms = [x**4 for x in range(1, 1000)]
%o A345593 for pos in cwr(power_terms, 9):
%o A345593     tot = sum(pos)
%o A345593     keep[tot] += 1
%o A345593     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345593     for x in range(len(rets)):
%o A345593         print(rets[x])
%Y A345593 Cf. A345548, A345584, A345592, A345594, A345602, A345626, A345851.
%K A345593 nonn
%O A345593 1,1
%A A345593 _David Consiglio, Jr._, Jun 20 2021