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a(n) = floor(sqrt(pi(2^n))).
1

%I #10 Jan 13 2017 18:46:46

%S 0,1,1,2,2,3,4,5,7,9,13,17,23,32,43,59,80,110,151,208,286,394,544,751,

%T 1038,1436,1989,2757,3825,5309,7375,10251,14257,19839,27621,38473,

%U 53613,74742,104241,145436,202985,283401,395804,552957,772733,1080160,1510297

%N a(n) = floor(sqrt(pi(2^n))).

%H G. C. Greubel, <a href="/A133498/b133498.txt">Table of n, a(n) for n = 0..86</a>

%F a(n) = floor(sqrt(A007053(n))).

%e a(4)=2 because pi(2^4)=6 and the greatest integer less than or equal to sqrt(6) is 2.

%t Table[ Floor[Sqrt[PrimePi[2^n]]], {n, 0, 25}] (* _G. C. Greubel_, Jan 13 2017 *)

%o (PARI) a(n) = sqrtint(primepi(2^n)); \\ _Michel Marcus_, Sep 05 2013

%Y Cf. A000720, A007053.

%K nonn

%O 0,4

%A _Andrew V. Sutherland_, Dec 01 2007