cp's OEIS Frontend

A345594 Numbers that are the sum of nine fourth powers in ten or more ways.

%I A345594 #6 Jul 31 2021 17:39:23
%S A345594 9299,12708,12948,13269,13349,13524,13589,13764,13829,13893,14133,
%T A345594 14228,14468,14564,14804,14869,14934,14964,15014,15044,15094,15109,
%U A345594 15174,15189,15333,15413,15428,15429,15443,15508,15524,15573,15588,15604,15653,15669,15683
%N A345594 Numbers that are the sum of nine fourth powers in ten or more ways.
%H A345594 Sean A. Irvine, <a href="/A345594/b345594.txt">Table of n, a(n) for n = 1..10000</a>
%e A345594 12708 is a term because 12708 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 10^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 10^4 = 1^4 + 1^4 + 1^4 + 5^4 + 6^4 + 6^4 + 6^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 9^4 = 1^4 + 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 9^4 = 1^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 10^4 = 2^4 + 2^4 + 3^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 5^4 + 7^4 + 7^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 7^4 + 8^4.
%o A345594 (Python)
%o A345594 from itertools import combinations_with_replacement as cwr
%o A345594 from collections import defaultdict
%o A345594 keep = defaultdict(lambda: 0)
%o A345594 power_terms = [x**4 for x in range(1, 1000)]
%o A345594 for pos in cwr(power_terms, 9):
%o A345594     tot = sum(pos)
%o A345594     keep[tot] += 1
%o A345594     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345594     for x in range(len(rets)):
%o A345594         print(rets[x])
%Y A345594 Cf. A345549, A345585, A345593, A345603, A345627, A345852.
%K A345594 nonn
%O A345594 1,1
%A A345594 _David Consiglio, Jr._, Jun 20 2021