cp's OEIS Frontend

A345583 Numbers that are the sum of eight fourth powers in eight or more ways.

%I A345583 #6 Jul 31 2021 17:51:48
%S A345583 13268,14212,14788,15427,15667,16612,16627,16692,16707,16772,16822,
%T A345583 16852,16882,16947,17348,17363,17428,17493,17877,17972,17987,18052,
%U A345583 18117,18227,18948,19157,19237,19252,19267,19412,19492,19507,19572,19682,19747,19748,19828
%N A345583 Numbers that are the sum of eight fourth powers in eight or more ways.
%H A345583 Sean A. Irvine, <a href="/A345583/b345583.txt">Table of n, a(n) for n = 1..10000</a>
%e A345583 14212 is a term because 14212 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 8^4 + 10^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 7^4 + 10^4 = 1^4 + 1^4 + 1^4 + 5^4 + 6^4 + 8^4 + 8^4 + 8^4 = 1^4 + 2^4 + 4^4 + 4^4 + 5^4 + 7^4 + 8^4 + 9^4 = 1^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 8^4 + 9^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 + 10^4 = 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 10^4 = 3^4 + 4^4 + 4^4 + 5^4 + 7^4 + 7^4 + 8^4 + 8^4.
%o A345583 (Python)
%o A345583 from itertools import combinations_with_replacement as cwr
%o A345583 from collections import defaultdict
%o A345583 keep = defaultdict(lambda: 0)
%o A345583 power_terms = [x**4 for x in range(1, 1000)]
%o A345583 for pos in cwr(power_terms, 8):
%o A345583     tot = sum(pos)
%o A345583     keep[tot] += 1
%o A345583     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345583     for x in range(len(rets)):
%o A345583         print(rets[x])
%Y A345583 Cf. A345538, A345574, A345582, A345584, A345592, A345616, A345840.
%K A345583 nonn
%O A345583 1,1
%A A345583 _David Consiglio, Jr._, Jun 20 2021