cp's OEIS Frontend

A345837 Numbers that are the sum of eight fourth powers in exactly five ways.

%I A345837 #6 Jul 31 2021 21:33:37
%S A345837 4228,4403,4468,5443,5508,5683,6613,6643,6658,6708,6773,6838,6868,
%T A345837 6883,6948,7013,7093,7138,7203,7267,7268,7332,7397,7478,7507,7572,
%U A345837 7588,7828,7858,7923,7988,8113,8133,8228,8353,8418,8533,8547,8548,8612,8723,8788,8852
%N A345837 Numbers that are the sum of eight fourth powers in exactly five ways.
%C A345837 Differs from A345580 at term 11 because 6723 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 6^4 + 6^4 + 8^4  = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4  = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4  = 2^4 + 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4  = 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4  = 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4.
%H A345837 Sean A. Irvine, <a href="/A345837/b345837.txt">Table of n, a(n) for n = 1..10000</a>
%e A345837 4403 is a term because 4403 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4.
%o A345837 (Python)
%o A345837 from itertools import combinations_with_replacement as cwr
%o A345837 from collections import defaultdict
%o A345837 keep = defaultdict(lambda: 0)
%o A345837 power_terms = [x**4 for x in range(1, 1000)]
%o A345837 for pos in cwr(power_terms, 8):
%o A345837     tot = sum(pos)
%o A345837     keep[tot] += 1
%o A345837     rets = sorted([k for k, v in keep.items() if v == 5])
%o A345837     for x in range(len(rets)):
%o A345837         print(rets[x])
%Y A345837 Cf. A345580, A345787, A345827, A345836, A345838, A345847, A346330.
%K A345837 nonn
%O A345837 1,1
%A A345837 _David Consiglio, Jr._, Jun 26 2021