cp's OEIS Frontend

A345818 Numbers that are the sum of six fourth powers in exactly six ways.

%I A345818 #6 Jul 31 2021 21:57:26
%S A345818 37811,38051,43251,43571,44115,44531,45155,45651,45891,47411,47586,
%T A345818 49971,52195,53235,54131,56290,57395,57460,57570,59075,59330,59860,
%U A345818 60035,62180,62211,63971,66340,67026,67635,67715,67860,67940,68115,68291,68484,69395,69410
%N A345818 Numbers that are the sum of six fourth powers in exactly six ways.
%C A345818 Differs from A345563 at term 1 because 21251 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 12^4  = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4  = 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4  = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4  = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4  = 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4  = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4.
%H A345818 Sean A. Irvine, <a href="/A345818/b345818.txt">Table of n, a(n) for n = 1..10000</a>
%e A345818 37811 is a term because 37811 = 1^4 + 2^4 + 2^4 + 7^4 + 11^4 + 12^4 = 2^4 + 2^4 + 4^4 + 7^4 + 9^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 9^4 + 13^4 = 3^4 + 4^4 + 8^4 + 8^4 + 11^4 + 11^4 = 4^4 + 6^4 + 7^4 + 9^4 + 9^4 + 12^4 = 5^4 + 5^4 + 9^4 + 10^4 + 10^4 + 10^4.
%o A345818 (Python)
%o A345818 from itertools import combinations_with_replacement as cwr
%o A345818 from collections import defaultdict
%o A345818 keep = defaultdict(lambda: 0)
%o A345818 power_terms = [x**4 for x in range(1, 1000)]
%o A345818 for pos in cwr(power_terms, 6):
%o A345818     tot = sum(pos)
%o A345818     keep[tot] += 1
%o A345818     rets = sorted([k for k, v in keep.items() if v == 6])
%o A345818     for x in range(len(rets)):
%o A345818         print(rets[x])
%Y A345818 Cf. A344941, A345563, A345768, A345817, A345819, A345828, A346361.
%K A345818 nonn
%O A345818 1,1
%A A345818 _David Consiglio, Jr._, Jun 26 2021