cp's OEIS Frontend

A129843 a(n) = number of positive integers that are <= n and are coprime to n!! (n!! = A006882(n)).

%I A129843 #17 Dec 12 2022 16:03:13
%S A129843 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 A129843 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 A129843 7,9,7,10,7,10,7,10,7,10,7,11
%N A129843 a(n) = number of positive integers that are <= n and are coprime to n!! (n!! = A006882(n)).
%H A129843 Robert Israel, <a href="/A129843/b129843.txt">Table of n, a(n) for n = 1..10000</a>
%F A129843 From _Robert Israel_, Dec 08 2022: (Start)
%F A129843 If n is odd, a(n) = A070939(n).
%F A129843 If n > 2 is even, a(n) = 1 + A056171(n). (End)
%p A129843 f:= proc(n) local t;
%p A129843      if n::odd then ilog2(n)+1
%p A129843      else 1+numtheory:-pi(n) - numtheory:-pi(n/2)
%p A129843      fi
%p A129843 end proc:
%p A129843 f(2):= 1:
%p A129843 map(f, [$1..100]); # _Robert Israel_, Dec 08 2022
%t A129843 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 A129843 Table[Total[Boole[CoprimeQ[n!!,Range[n]]]],{n,80}] (* _Harvey P. Dale_, Dec 12 2022 *)
%Y A129843 Cf. A006882, A056171, A070939.
%K A129843 nonn
%O A129843 1,3
%A A129843 _Leroy Quet_, Jun 03 2007
%E A129843 More terms from _Stefan Steinerberger_, Jun 05 2007