cp's OEIS Frontend

A345819 Numbers that are the sum of six fourth powers in exactly seven ways.

%I A345819 #6 Jul 31 2021 21:57:29
%S A345819 21251,43875,48276,49796,53315,58500,59795,59811,67875,68306,69155,
%T A345819 69779,71955,72051,72131,73970,74420,74851,77010,80291,80515,81875,
%U A345819 82275,84515,86436,86451,86531,87075,88355,88660,88675,90355,91475,93410,93650,94690,95155
%N A345819 Numbers that are the sum of six fourth powers in exactly seven ways.
%C A345819 Differs from A345564 at term 6 because 58035 = 1^4 + 1^4 + 9^4 + 10^4 + 12^4 + 12^4  = 1^4 + 4^4 + 5^4 + 8^4 + 11^4 + 14^4  = 1^4 + 5^4 + 6^4 + 11^4 + 12^4 + 12^4  = 2^4 + 2^4 + 4^4 + 5^4 + 13^4 + 13^4  = 2^4 + 6^4 + 6^4 + 7^4 + 7^4 + 15^4  = 2^4 + 8^4 + 10^4 + 11^4 + 11^4 + 11^4  = 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 15^4  = 4^4 + 5^4 + 6^4 + 9^4 + 12^4 + 13^4.
%H A345819 Sean A. Irvine, <a href="/A345819/b345819.txt">Table of n, a(n) for n = 1..10000</a>
%e A345819 43875 is a term because 43875 = 1^4 + 2^4 + 9^4 + 9^4 + 10^4 + 12^4 = 2^4 + 2^4 + 2^4 + 5^4 + 11^4 + 13^4 = 2^4 + 2^4 + 5^4 + 7^4 + 7^4 + 14^4 = 2^4 + 5^4 + 6^4 + 9^4 + 11^4 + 12^4 = 3^4 + 7^4 + 8^4 + 9^4 + 10^4 + 12^4 = 4^4 + 4^4 + 7^4 + 7^4 + 10^4 + 13^4 = 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.
%o A345819 (Python)
%o A345819 from itertools import combinations_with_replacement as cwr
%o A345819 from collections import defaultdict
%o A345819 keep = defaultdict(lambda: 0)
%o A345819 power_terms = [x**4 for x in range(1, 1000)]
%o A345819 for pos in cwr(power_terms, 6):
%o A345819     tot = sum(pos)
%o A345819     keep[tot] += 1
%o A345819     rets = sorted([k for k, v in keep.items() if v == 7])
%o A345819     for x in range(len(rets)):
%o A345819         print(rets[x])
%Y A345819 Cf. A344943, A345564, A345769, A345818, A345820, A345829, A346362.
%K A345819 nonn
%O A345819 1,1
%A A345819 _David Consiglio, Jr._, Jun 26 2021