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A097051 a(n) = floor(n/a(floor(n/2))); a(1) = 1.

%I A097051 #14 Jan 06 2021 18:35:24
%S A097051 1,2,3,2,2,2,2,4,4,5,5,6,6,7,7,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,
%T A097051 8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,
%U A097051 14,15,15,15,15,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
%N A097051 a(n) = floor(n/a(floor(n/2))); a(1) = 1.
%H A097051 Robert Israel, <a href="/A097051/b097051.txt">Table of n, a(n) for n = 1..10000</a>
%F A097051 If floor(log_2(n))=2k+1, then a(n) = floor(n/2^k). If floor(log_2(n))=2k, then a(n) = 2^k.
%e A097051 a(50)=floor(50/a(25))
%e A097051 ..... a(25)=floor(25/a(12))
%e A097051 ........... a(12)=floor(12/a(6))
%e A097051 ................. a(6)=floor(6/a(3))
%e A097051 ...................... a(3)=floor(3/a(1))
%e A097051 ........................... a(1)=1
%e A097051 ...................... a(3)=floor(3/a(1))=floor(3/1)=3
%e A097051 ................. a(6)=floor(6/a(3))=floor(6/3)=2
%e A097051 ........... a(12)=floor(12/a(6))=floor(12/2)=6
%e A097051 ..... a(25)=floor(25/a(12))=floor(25/6)=4
%e A097051 a(50)=floor(50/a(25))=floor(50/4)=12.
%p A097051 f:= proc(n) option remember;  floor(n/procname(floor(n/2))) end proc:
%p A097051 f(1):= 1:
%p A097051 map(f, [$1..200]); # _Robert Israel_, Jan 06 2021
%t A097051 a[1] = 1; a[n_] := a[n] = Floor[n/a[Floor[n/2]]]; Table[ a[n], {n, 94}]
%Y A097051 Cf. A096036, A097053.
%K A097051 nonn
%O A097051 1,2
%A A097051 _Reinhard Zumkeller_ and _Robert G. Wilson v_, Jul 21 2004
%E A097051 Formula added by _Max Alekseyev_, Mar 02 2011