cp's OEIS Frontend

A345584 Numbers that are the sum of eight fourth powers in nine or more ways.

%I A345584 #6 Jul 31 2021 17:51:52
%S A345584 15427,16692,17348,17493,17972,17987,18052,18227,19267,19412,19492,
%T A345584 19507,19572,19747,19748,20116,20787,20852,21268,21283,21333,21348,
%U A345584 21413,21443,21493,21508,21523,21588,21637,21652,21653,21827,21877,21892,21957,21972,22037
%N A345584 Numbers that are the sum of eight fourth powers in nine or more ways.
%H A345584 Sean A. Irvine, <a href="/A345584/b345584.txt">Table of n, a(n) for n = 1..10000</a>
%e A345584 16692 is a term because 16692 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4 = 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 5^4 + 7^4 + 9^4 + 9^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 9^4 + 9^4.
%o A345584 (Python)
%o A345584 from itertools import combinations_with_replacement as cwr
%o A345584 from collections import defaultdict
%o A345584 keep = defaultdict(lambda: 0)
%o A345584 power_terms = [x**4 for x in range(1, 1000)]
%o A345584 for pos in cwr(power_terms, 8):
%o A345584     tot = sum(pos)
%o A345584     keep[tot] += 1
%o A345584     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345584     for x in range(len(rets)):
%o A345584         print(rets[x])
%Y A345584 Cf. A345539, A345575, A345583, A345585, A345593, A345617, A345841.
%K A345584 nonn
%O A345584 1,1
%A A345584 _David Consiglio, Jr._, Jun 20 2021