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A344358 Numbers that are the sum of five fourth powers in five or more ways.

%I A344358 #12 Jul 31 2021 18:13:24
%S A344358 59779,67859,93394,108274,112850,136915,142354,151300,151475,161459,
%T A344358 168979,181219,183539,183604,185299,187699,189394,193379,195394,
%U A344358 197779,199090,199474,200979,201874,202979,203299,205859,211059,211330,212419,213730,217154,217810,217890,221779,223090,223155
%N A344358 Numbers that are the sum of five fourth powers in five or more ways.
%H A344358 David Consiglio, Jr., <a href="/A344358/b344358.txt">Table of n, a(n) for n = 1..20000</a>
%e A344358 93394 is a term of this sequence because 93394 = 1^4 + 4^4 + 8^4 + 14^4 + 15^4 = 1^4 + 6^4 + 12^4 + 12^4 + 15^4 = 1^4 + 9^4 + 10^4 + 14^4 + 14^4 = 5^4 + 6^4 + 11^4 + 14^4 + 14^4 = 5^4 + 7^4 + 8^4 + 12^4 + 16^4.
%o A344358 (Python)
%o A344358 from itertools import combinations_with_replacement as cwr
%o A344358 from collections import defaultdict
%o A344358 keep = defaultdict(lambda: 0)
%o A344358 power_terms = [x**4 for x in range(1, 50)]
%o A344358 for pos in cwr(power_terms, 5):
%o A344358     tot = sum(pos)
%o A344358     keep[tot] += 1
%o A344358 rets = sorted([k for k, v in keep.items() if v >= 5])
%o A344358 for x in range(len(rets)):
%o A344358     print(rets[x])
%Y A344358 Cf. A343989, A344354, A344356, A344359, A344940, A345562, A345863.
%K A344358 nonn
%O A344358 1,1
%A A344358 _David Consiglio, Jr._, May 15 2021