A124446 a(n) = gcd(A066840(n), A124440(n)).

1, 1, 1, 1, 1, 1, 3, 4, 1, 4, 5, 6, 3, 3, 2, 16, 4, 1, 9, 20, 6, 5, 11, 24, 1, 12, 1, 42, 7, 8, 15, 64, 10, 16, 6, 54, 9, 9, 6, 80, 10, 6, 21, 110, 2, 11, 23, 96, 3, 4, 8, 156, 13, 1, 10, 168, 18, 28, 29, 120, 15, 15, 6, 256, 24, 10, 33, 272, 22, 24, 35, 216, 18, 36, 2, 342, 30, 24, 39

Offset: 1

Author

Leroy Quet, Nov 01 2006

Keywords

• nonn

Examples

			Those positive integers which are coprime to 8 and are <= 8/2, are 1 and 3. Those integers which are coprime to 8 and are between 8/2 and 8, are 5 and 7.
So a(8) = gcd(1+3, 5+7) = gcd(4, 12) = 4.
		

Links

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

Crossrefs

Cf. A066840, A124440, A124447.

Programs

Maple

N:= 100: # for a(1)..a(N)
G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2),n=1..N/2):
S:= series(G,x,N+1):
A66840:= [seq(coeff(S,x,j),j=1..N)]:
[1,1,seq(igcd(A66840[n], n*numtheory:-phi(n)/2),n=3..N)]; # Robert Israel, Feb 02 2021

Mathematica

f1[n_] := Plus @@ Select[Range[Floor[n/2]], GCD[ #,n] == 1 &]; f2[n_] := Plus @@ Select[Range[Ceiling[n/2], n], GCD[ #, n] == 1 &];Table[GCD[f1[n], f2[n]], {n, 80}] (* Ray Chandler, Nov 12 2006 *)

Extensions

Extended by Ray Chandler, Nov 12 2006