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a(n) = 2*n^4 - floor(2^(1/4)*n)^4.
2

%I #13 Aug 07 2023 03:55:56

%S 0,1,16,81,256,625,191,706,1631,3122,5359,721,3056,6497,11296,17729,

%T 751,7042,15471,26386,40159,57186,11536,28241,48896,73969,103952,

%U 14306,43391,78226,119375,167426,12016,58401,112672,175489,247536,226,69647,149426,240319

%N a(n) = 2*n^4 - floor(2^(1/4)*n)^4.

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

%e a(5) = 2*5^4 - floor(2^(1/4)*5)^4 = 2*625 - 5^4 = 625.

%e a(6) = 2*6^4 - floor(2^(1/4)*6)^4 = 2*1296 - 7^4 = 191.

%t Table[2 n^4 - Floor[2^(1/4) n]^4, {n, 0, 60}] (* _Vincenzo Librandi_, May 29 2015 *)

%o (PARI) f(n,e=4,b=2)=n^e*b-floor(sqrtn(b,e)*n)^e

%o (Magma) [2*n^4 - Floor(2^(1/4)*n)^4: n in [0..50]]; // _Vincenzo Librandi_, May 29 2015

%Y Cf. A087056 (analog for squares), A257853 & A257855 (3rd & 5th power).

%K nonn,easy

%O 0,3

%A _M. F. Hasler_, May 28 2015