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A344354 Numbers that are the sum of five fourth powers in four or more ways.

%I A344354 #12 Jul 31 2021 18:13:20
%S A344354 20995,21235,31250,41474,43235,43250,43315,43490,43859,45139,46290,
%T A344354 47570,51939,53234,53299,54994,56274,57379,57410,57779,59329,59779,
%U A344354 63970,67010,67859,68035,68290,71795,71954,73730,73954,75714,75794,77890,82099,84499,86275,86450,87730,92500,93394,93474,93859
%N A344354 Numbers that are the sum of five fourth powers in four or more ways.
%H A344354 David Consiglio, Jr., <a href="/A344354/b344354.txt">Table of n, a(n) for n = 1..20000</a>
%e A344354 31250 is a term of this sequence because 31250 = 2^4 + 2^4 + 4^4 + 7^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 13^4 = 4^4 + 6^4 + 7^4 + 9^4 + 12^4 = 5^4 + 5^4 + 10^4 + 10^4 + 10^4.
%o A344354 (Python)
%o A344354 from itertools import combinations_with_replacement as cwr
%o A344354 from collections import defaultdict
%o A344354 keep = defaultdict(lambda: 0)
%o A344354 power_terms = [x**4 for x in range(1, 50)]
%o A344354 for pos in cwr(power_terms, 5):
%o A344354     tot = sum(pos)
%o A344354     keep[tot] += 1
%o A344354 rets = sorted([k for k, v in keep.items() if v >= 4])
%o A344354 for x in range(len(rets)):
%o A344354     print(rets[x])
%Y A344354 Cf. A344034, A344243, A344352, A344355, A344358, A344518, A345561.
%K A344354 nonn
%O A344354 1,1
%A A344354 _David Consiglio, Jr._, May 15 2021