A219029 a(n) = n - 1 - phi(phi(n)).

-1, 0, 1, 2, 2, 4, 4, 5, 6, 7, 6, 9, 8, 11, 10, 11, 8, 15, 12, 15, 16, 17, 12, 19, 16, 21, 20, 23, 16, 25, 22, 23, 24, 25, 26, 31, 24, 31, 30, 31, 24, 37, 30, 35, 36, 35, 24, 39, 36, 41, 34, 43, 28, 47, 38, 47, 44, 45, 30, 51, 44, 53, 50, 47, 48, 57, 46, 51, 48

Offset: 1

Author

V. Raman, Nov 10 2012

Keywords

• sign

Comments

There are exactly n - 1 - phi(phi(n)) non-primitive roots for n, less than n, if n is prime.

a(n) will be the same as A219027(n) except when n is a member of A033949 or n = 1, i.e., n is not 2, 4, prime, power of a prime, twice a prime, or twice a prime power.

Links

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

Crossrefs

Cf. A008330 (number of primitive roots for the n-th prime).

Cf. A046144 (number of primitive roots for n).

Cf. A010554 (value of phi(phi(n))).

Cf. A219027, A219428.

Programs

Magma

[(n - 1 - EulerPhi(EulerPhi(n))): n in [1..70] ]; // Vincenzo Librandi, Jan 26 2013

Mathematica

Table[n - (EulerPhi[EulerPhi[n]] + 1), {n, 75}] (* Alonso del Arte, Nov 17 2012 *)

PARI

for(n=1,100,print1(n-1-eulerphi(eulerphi(n))","))

Formula

a(n) = n - 1 - A010554(n). - V. Raman, Nov 22 2012