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A342685 Numbers that are the sum of five fifth powers in two or more ways.

%I A342685 #19 May 10 2024 16:50:54
%S A342685 4097,51446,51477,51688,52469,54570,59221,68252,68905,84213,110494,
%T A342685 131104,151445,212496,300277,325174,325713,355114,422135,422738,
%U A342685 589269,637418,794434,810820,876734,876765,876976,877757,879858,884509,893540,909501,924912,935782,976733,995571,1037784,1083457
%N A342685 Numbers that are the sum of five fifth powers in two or more ways.
%H A342685 David Consiglio, Jr., <a href="/A342685/b342685.txt">Table of n, a(n) for n = 1..20000</a>
%e A342685 51477 = 2^5 + 4^5 + 7^5 + 7^5 + 7^5
%e A342685       = 2^5 + 5^5 + 6^5 + 6^5 + 8^5
%e A342685 so 51477 is a term.
%o A342685 (Python)
%o A342685 from itertools import combinations_with_replacement as cwr
%o A342685 from collections import defaultdict
%o A342685 keep = defaultdict(lambda: 0)
%o A342685 power_terms = [x**5 for x in range(1, 500)]
%o A342685 for pos in cwr(power_terms, 5):
%o A342685     tot = sum(pos)
%o A342685     keep[tot] += 1
%o A342685 rets = sorted([k for k, v in keep.items() if v >= 2])
%o A342685 for x in range(len(rets)):
%o A342685     print(rets[x])
%Y A342685 Cf. A003350, A342686, A342687, A344238, A344644, A345507.
%K A342685 nonn
%O A342685 1,1
%A A342685 _David Consiglio, Jr._, May 17 2021