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

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, 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, 7, 9, 7, 10, 7, 10, 7, 10, 7, 10, 7, 11

Offset: 1

Author

Leroy Quet, Jun 03 2007

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006882, A056171, A070939.

Programs

Maple

f:= proc(n) local t;
     if n::odd then ilog2(n)+1
     else 1+numtheory:-pi(n) - numtheory:-pi(n/2)
     fi
end proc:
f(2):= 1:
map(f, [$1..100]); # Robert Israel, Dec 08 2022

Mathematica

a[n_]:=Module[{},co=0;For[i=1,iStefan Steinerberger, Jun 05 2007 *)
Table[Total[Boole[CoprimeQ[n!!,Range[n]]]],{n,80}] (* Harvey P. Dale, Dec 12 2022 *)

Formula

From Robert Israel, Dec 08 2022: (Start)

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

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

Extensions

More terms from Stefan Steinerberger, Jun 05 2007