A089692 - OEIS

%I #20 Jun 30 2023 04:56:25

%S 1,1,1,2,2,1,3,4,3,2,5,2,6,3,2,8,8,3,9,4,3,5,11,4,10,6,9,6,14,2,15,16,

%T 5,8,6,6,18,9,6,8,20,3,21,10,6,11,23,8,21,10,8,12,26,9,10,12,9,14,29,

%U 4,30,15,9,32,12,5,33,16,11,6,35,12,36,18,10,18,15,6,39,16,27,20,41,6,16,21

%N a(n) = phi(2n)/2^omega(n).

%C Here omega(n) means the number of prime factors of n counted without multiplicity. - _Harvey P. Dale_, Dec 12 2012

%H Amiram Eldar, <a href="/A089692/b089692.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A062570(n)/A034444(n).

%F Multiplicative with a(2^e) = 2^(e-1) and a(p^e) = (p^e-p^(e-1))/2 for an odd prime p. - _Vladeta Jovovic_, Jan 15 2004

%F a(n) = A000010(n)/2^A005087(n). - _Michel Marcus_, Jun 30 2023

%t Table[EulerPhi[2n]/2^PrimeNu[n],{n,90}] (* _Harvey P. Dale_, Dec 12 2012 *)

%t f[p_, e_] := If[p == 2, 2^(e-1), (p^e-p^(e-1))/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 09 2022 *)

%Y Cf. A000010, A005087, A001221, A034444, A062570.

%K nonn,mult

%O 1,4

%A _Benoit Cloitre_, Jan 06 2004