A129843 - OEIS

%I #17 Dec 12 2022 16:03:13

%S 1,1,2,2,3,2,3,3,4,2,4,3,4,3,4,3,5,4,5,5,5,4,5,5,5,4,5,4,5,5,5,6,6,5,

%T 6,5,6,5,6,5,6,6,6,7,6,6,6,7,6,7,6,7,6,8,6,8,6,7,6,8,6,8,6,8,7,8,7,9,

%U 7,9,7,10,7,10,7,10,7,10,7,11

%N a(n) = number of positive integers that are <= n and are coprime to n!! (n!! = A006882(n)).

%H Robert Israel, <a href="/A129843/b129843.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Robert Israel_, Dec 08 2022: (Start)

%F If n is odd, a(n) = A070939(n).

%F If n > 2 is even, a(n) = 1 + A056171(n). (End)

%p f:= proc(n) local t;

%p      if n::odd then ilog2(n)+1

%p      else 1+numtheory:-pi(n) - numtheory:-pi(n/2)

%p      fi

%p end proc:

%p f(2):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Dec 08 2022

%t a[n_]:=Module[{},co=0;For[i=1,i<n+1,i++,If[GCD[n!!,i]==1,co++ ]];co]; Table[a[n], {n, 1, 80}] (* _Stefan Steinerberger_, Jun 05 2007 *)

%t Table[Total[Boole[CoprimeQ[n!!,Range[n]]]],{n,80}] (* _Harvey P. Dale_, Dec 12 2022 *)

%Y Cf. A006882, A056171, A070939.

%K nonn

%O 1,3

%A _Leroy Quet_, Jun 03 2007

%E More terms from _Stefan Steinerberger_, Jun 05 2007