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A344356 Numbers that are the sum of four fourth powers in five or more ways.

%I A344356 #12 Jul 31 2021 18:21:58
%S A344356 2147874,2266338,2690658,3189603,3464178,3754674,3847554,4030419,
%T A344356 4165794,4457298,4884114,5229378,5624739,5978883,5980178,5981283,
%U A344356 6014178,6044418,6134994,6258723,6313953,6400194,6576339,6593538,6612354,6899603,7088898,7498323,7811874,7918498,8064018,8292323
%N A344356 Numbers that are the sum of four fourth powers in five or more ways.
%H A344356 David Consiglio, Jr., <a href="/A344356/b344356.txt">Table of n, a(n) for n = 1..20000</a>
%e A344356 2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.
%o A344356 (Python)
%o A344356 from itertools import combinations_with_replacement as cwr
%o A344356 from collections import defaultdict
%o A344356 keep = defaultdict(lambda: 0)
%o A344356 power_terms = [x**4 for x in range(1, 50)]
%o A344356 for pos in cwr(power_terms, 4):
%o A344356     tot = sum(pos)
%o A344356     keep[tot] += 1
%o A344356 rets = sorted([k for k, v in keep.items() if v >= 5])
%o A344356 for x in range(len(rets)):
%o A344356     print(rets[x])
%Y A344356 Cf. A343987, A344352, A344357, A344358, A344364, A344904.
%K A344356 nonn
%O A344356 1,1
%A A344356 _David Consiglio, Jr._, May 15 2021