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A124446 a(n) = gcd(A066840(n), A124440(n)). 5

%I #14 Feb 02 2021 18:24:36

%S 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,

%T 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,

%U 18,28,29,120,15,15,6,256,24,10,33,272,22,24,35,216,18,36,2,342,30,24,39

%N a(n) = gcd(A066840(n), A124440(n)).

%H Robert Israel, <a href="/A124446/b124446.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%e So a(8) = gcd(1+3, 5+7) = gcd(4, 12) = 4.

%p N:= 100: # for a(1)..a(N)

%p G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2),n=1..N/2):

%p S:= series(G,x,N+1):

%p A66840:= [seq(coeff(S,x,j),j=1..N)]:

%p [1,1,seq(igcd(A66840[n], n*numtheory:-phi(n)/2),n=3..N)]; # _Robert Israel_, Feb 02 2021

%t 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 *)

%Y Cf. A066840, A124440, A124447.

%K nonn

%O 1,7

%A _Leroy Quet_, Nov 01 2006

%E Extended by _Ray Chandler_, Nov 12 2006

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)