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A344190 Numbers that are the sum of five fourth powers in exactly one way.

%I A344190 #10 Jul 31 2021 22:02:46
%S A344190 5,20,35,50,65,80,85,100,115,130,145,165,180,195,210,245,290,305,320,
%T A344190 325,355,370,385,405,420,435,450,500,530,545,560,580,595,610,625,629,
%U A344190 644,659,674,675,689,690,709,724,739,754,755,770,785,789,800,804,819,850,865,869,899,914,929,930,949,964,979,994,1025,1040
%N A344190 Numbers that are the sum of five fourth powers in exactly one way.
%C A344190 Differs from A003339 at term 17 because 260 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4
%H A344190 David Consiglio, Jr., <a href="/A344190/b344190.txt">Table of n, a(n) for n = 1..20000</a>
%e A344190 35 is a member of this sequence because 35 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4
%o A344190 (Python)
%o A344190 from itertools import combinations_with_replacement as cwr
%o A344190 from collections import defaultdict
%o A344190 keep = defaultdict(lambda: 0)
%o A344190 power_terms = [x**4 for x in range(1,50)]
%o A344190 for pos in cwr(power_terms,5):
%o A344190     tot = sum(pos)
%o A344190     keep[tot] += 1
%o A344190 rets = sorted([k for k,v in keep.items() if v == 1])
%o A344190 for x in range(len(rets)):
%o A344190     print(rets[x])
%Y A344190 Cf. A003339, A048926, A344189, A344237, A344643, A345813.
%K A344190 nonn
%O A344190 1,1
%A A344190 _David Consiglio, Jr._, May 11 2021