

A020896


Positive numbers n such that n = x^5 + y^5 has a solution in nonzero integers x, y.


2



2, 31, 33, 64, 211, 242, 244, 275, 486, 781, 992, 1023, 1025, 1056, 1267, 2048, 2101, 2882, 3093, 3124, 3126, 3157, 3368, 4149, 4651, 6250, 6752, 7533, 7744, 7775, 7777, 7808, 8019, 8800, 9031, 10901, 13682, 15552, 15783, 15961, 16564
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OFFSET

0,1


COMMENTS

68101 = (15/2)^5 + (17/2)^5 is believed to be the smallest positive integer n which is the sum of two nonzero fifth powers of rational numbers but not the sum of two nonzero fifth powers of integers.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
J.P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99.
S. R. Finch, On a Generalized FermatWiles Equation


FORMULA

See Theorem 3.5.6 of J.P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 99.


EXAMPLE

E.g. 31 = 2^5 + (1)^5.


MATHEMATICA

Select[Union[Total/@(Select[Tuples[Range[8, 8], {2}], !MemberQ[#, 0]&]^5)], #>0&] (* Harvey P. Dale, Apr 03 2011 *)


CROSSREFS

Cf. A001481, A020897, A003336.
Sequence in context: A099189 A247099 A053234 * A042153 A267207 A102630
Adjacent sequences: A020893 A020894 A020895 * A020897 A020898 A020899


KEYWORD

nonn,nice


AUTHOR

Steven Finch


STATUS

approved



