A109606 Number of numbers k with 1 < k < n which are relatively prime to n.

0, 0, 1, 1, 3, 1, 5, 3, 5, 3, 9, 3, 11, 5, 7, 7, 15, 5, 17, 7, 11, 9, 21, 7, 19, 11, 17, 11, 27, 7, 29, 15, 19, 15, 23, 11, 35, 17, 23, 15, 39, 11, 41, 19, 23, 21, 45, 15, 41, 19, 31, 23, 51, 17, 39, 23, 35, 27, 57, 15, 59, 29, 35, 31, 47, 19, 65, 31, 43, 23, 69, 23, 71, 35, 39, 35

Offset

1,5

Comments

Number of nonprincipal Dirichlet characters mod n. - Charles R Greathouse IV, Jul 25 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Formula

a(n) = phi(n) - 1 = A000010(n) - 1.

a(n) = card({k| k prime to n} setminus {k| k divides n}). - Peter Luschny, Aug 05 2011

G.f.: -x/(1 - x) + Sum_{k >= 1} mu(k)*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Mar 16 2017

Example

a(9) = 5 because 2, 4, 5, 7, 8 are coprime to 9.
a(10) = 3 because 3, 7, 9 are coprime to 10.

Maple

A109606 := n -> numtheory[phi](n) - 1: # Peter Luschny, Aug 05 2011

Mathematica

EulerPhi[Range[80]] - 1 (* Alonso del Arte, Sep 16 2017 *)

Prog

(PARI) a(n)=eulerphi(n)-1 \\ Charles R Greathouse IV, Jul 25 2013
(Magma) [EulerPhi(n)-1: n in [1..80]]; // Vincenzo Librandi, Sep 16 2017

Crossrefs

Cf. A000010.

Sequence in context: A071168 A091926 A325685 * A318727 A307806 A127418

Adjacent sequences: A109603 A109604 A109605 * A109607 A109608 A109609

Keyword

nonn,easy

Author

Andrew Weimholt, Jul 31 2005

Extensions

Definition modified by Reinhard Zumkeller, Mar 03 2009

Offset set to 1, in accordance to A000010, by Peter Luschny, Aug 05 2011

Status

approved