A089692 a(n) = phi(2n)/2^omega(n).

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, 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, 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

Offset

1,4

Comments

Here omega(n) means the number of prime factors of n counted without multiplicity. - Harvey P. Dale, Dec 12 2012

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

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

a(n) = A000010(n)/2^A005087(n). - Michel Marcus, Jun 30 2023

Mathematica

Table[EulerPhi[2n]/2^PrimeNu[n], {n, 90}] (* Harvey P. Dale, Dec 12 2012 *)
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 *)

Crossrefs

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

Sequence in context: A105809 A091594 A118032 * A365519 A349346 A066201

Adjacent sequences: A089689 A089690 A089691 * A089693 A089694 A089695

Keyword

nonn,mult

Author

Benoit Cloitre, Jan 06 2004

Status

approved