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A344944 Numbers that are the sum of five fourth powers in eight or more ways.

%I A344944 #8 Jul 31 2021 18:13:38
%S A344944 534130,619090,654754,663155,729219,737459,742770,758354,775714,
%T A344944 810034,813459,816579,831250,906034,930499,954930,954979,1009954,
%U A344944 1055619,1083955,1099459,1100579,1101859,1103554,1106019,1157634,1167794,1179379,1180003,1186834
%N A344944 Numbers that are the sum of five fourth powers in eight or more ways.
%H A344944 David Consiglio, Jr., <a href="/A344944/b344944.txt">Table of n, a(n) for n = 1..10000</a>
%e A344944 534130 is a term because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4  = 2^4 + 2^4 + 4^4 + 7^4 + 27^4  = 2^4 + 3^4 + 6^4 + 6^4 + 27^4  = 2^4 + 6^4 + 9^4 + 21^4 + 24^4  = 4^4 + 16^4 + 17^4 + 18^4 + 23^4  = 6^4 + 8^4 + 11^4 + 22^4 + 23^4  = 7^4 + 8^4 + 16^4 + 19^4 + 24^4  = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.
%o A344944 (Python)
%o A344944 from itertools import combinations_with_replacement as cwr
%o A344944 from collections import defaultdict
%o A344944 keep = defaultdict(lambda: 0)
%o A344944 power_terms = [x**4 for x in range(1, 1000)]
%o A344944 for pos in cwr(power_terms, 5):
%o A344944     tot = sum(pos)
%o A344944     keep[tot] += 1
%o A344944 rets = sorted([k for k, v in keep.items() if v >= 8])
%o A344944 for x in range(len(rets)):
%o A344944     print(rets[x])
%Y A344944 Cf. A341891, A344922, A344924, A344942, A344945, A345183, A345565.
%K A344944 nonn
%O A344944 1,1
%A A344944 _David Consiglio, Jr._, Jun 03 2021