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%I #10 Jul 31 2021 22:02:46
%S 5,20,35,50,65,80,85,100,115,130,145,165,180,195,210,245,290,305,320,
%T 325,355,370,385,405,420,435,450,500,530,545,560,580,595,610,625,629,
%U 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 Numbers that are the sum of five fourth powers in exactly one way.
%C 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 David Consiglio, Jr., <a href="/A344190/b344190.txt">Table of n, a(n) for n = 1..20000</a>
%e 35 is a member of this sequence because 35 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**4 for x in range(1,50)]
%o for pos in cwr(power_terms,5):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k,v in keep.items() if v == 1])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A003339, A048926, A344189, A344237, A344643, A345813.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, May 11 2021
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