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A342686 Numbers that are the sum of five fifth powers in exactly two ways.

%I A342686 #21 May 11 2024 09:41:57
%S A342686 4097,51446,51477,51688,52469,54570,59221,68252,68905,84213,110494,
%T A342686 131104,151445,212496,300277,325174,325713,355114,422135,422738,
%U A342686 589269,637418,794434,810820,876734,876765,876976,877757,879858,884509,893540,909501,924912,935782,976733,995571,1037784,1083457
%N A342686 Numbers that are the sum of five fifth powers in exactly two ways.
%C A342686 This sequence differs from A342685:
%C A342686 13124675 =  1^5 +  9^5 + 10^5 + 20^5 + 25^5
%C A342686          =  2^5 +  5^5 + 12^5 + 23^5 + 23^5
%C A342686          = 16^5 + 19^5 + 20^5 + 20^5 + 20^5,
%C A342686 so 13124675 is in A342685, but is not in this sequence.
%H A342686 David Consiglio, Jr., <a href="/A342686/b342686.txt">Table of n, a(n) for n = 1..20000</a>
%e A342686 51477 = 2^5 + 4^5 + 7^5 + 7^5 + 7^5
%e A342686       = 2^5 + 5^5 + 6^5 + 6^5 + 8^5
%e A342686 so 51477 is a term of this sequence.
%o A342686 (Python)
%o A342686 from itertools import combinations_with_replacement as cwr
%o A342686 from collections import defaultdict
%o A342686 keep = defaultdict(lambda: 0)
%o A342686 power_terms = [x**5 for x in range(1, 500)]
%o A342686 for pos in cwr(power_terms, 5):
%o A342686     tot = sum(pos)
%o A342686     keep[tot] += 1
%o A342686 rets = sorted([k for k, v in keep.items() if v == 2])
%o A342686 for x in range(len(rets)):
%o A342686     print(rets[x])
%Y A342686 Cf. A342685, A342688, A344237, A344643, A344645, A346357.
%K A342686 nonn
%O A342686 1,1
%A A342686 _David Consiglio, Jr._, May 18 2021