cp's OEIS Frontend

A345585 Numbers that are the sum of eight fourth powers in ten or more ways.

%I A345585 #6 Jul 31 2021 17:51:55
%S A345585 17972,17987,19492,19507,19747,20116,20787,21268,21283,21333,21348,
%T A345585 21413,21508,21523,21588,21892,21957,22067,22132,22563,22628,23172,
%U A345585 23237,23252,23587,23588,23603,23653,23668,23733,23843,23908,24277,24452,24802,24948,25363
%N A345585 Numbers that are the sum of eight fourth powers in ten or more ways.
%H A345585 Sean A. Irvine, <a href="/A345585/b345585.txt">Table of n, a(n) for n = 1..10000</a>
%e A345585 17987 is a term because 17987 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 6^4 + 8^4 + 10^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 9^4 + 10^4 = 1^4 + 2^4 + 5^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 5^4 + 7^4 + 11^4 = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 6^4 + 11^4 = 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 7^4 + 8^4 + 10^4 = 2^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 + 10^4 = 2^4 + 4^4 + 5^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 = 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 + 10^4 = 3^4 + 5^4 + 6^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.
%o A345585 (Python)
%o A345585 from itertools import combinations_with_replacement as cwr
%o A345585 from collections import defaultdict
%o A345585 keep = defaultdict(lambda: 0)
%o A345585 power_terms = [x**4 for x in range(1, 1000)]
%o A345585 for pos in cwr(power_terms, 8):
%o A345585     tot = sum(pos)
%o A345585     keep[tot] += 1
%o A345585     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345585     for x in range(len(rets)):
%o A345585         print(rets[x])
%Y A345585 Cf. A345540, A345576, A345584, A345594, A345618, A345842.
%K A345585 nonn
%O A345585 1,1
%A A345585 _David Consiglio, Jr._, Jun 20 2021