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A257855 a(n) = 2*n^5 - floor(2^(1/5)*n)^5. 2

%I

%S 0,1,32,243,1024,3125,7776,846,6487,18098,38949,73270,126371,204762,

%T 27072,98893,207584,363615,579136,868097,1246368,205578,541639,991310,

%U 1576341,2320882,3251603,68663,866304,1886905,3164576,4736427,6642688,8926829,646649,2643750

%N a(n) = 2*n^5 - floor(2^(1/5)*n)^5.

%C Is there a simple expression for a nontrivial lower bound for a(n) ?

%e a(6) = 2*6^5 - floor(2^(1/5)*6)^5 = 2*7776 - 6^5 = 7776.

%e a(7) = 2*7^5 - floor(2^(1/5)*7)^5 = 2*16807 - 8^5 = 846.

%t Table[2 n^5 - Floor[2^(1/5) n]^5, {n, 0, 60}] (* _Vincenzo Librandi_, May 29 2015 *)

%o (PARI) f(n,e=5,b=2)=n^e*b-floor(sqrtn(b,e)*n)^e

%o (MAGMA) [2*n^5 - Floor(2^(1/5)*n)^5: n in [0..50]]; // _Vincenzo Librandi_, May 29 2015

%Y Cf. A087056 (analog for squares), A257853 - A257854 (3rd & 4th power).

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, May 28 2015

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)