

A219029


n  1  phi(phi(n)).


3



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
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OFFSET

1,4


COMMENTS

There are exactly n  1  phi(phi(n)) nonprimitive 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


FORMULA

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


MATHEMATICA

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


PROG

(PARI) for(n=1, 100, print1(n1eulerphi(eulerphi(n))", "))
(MAGMA) [(n  1  EulerPhi(EulerPhi(n))): n in [1..70] ]; // Vincenzo Librandi, Jan 26 2013


CROSSREFS

Cf. A008330 (number of primitive roots for the nth prime).
Cf. A046144 (number of primitive roots for n).
Cf. A010554 (value of phi(phi(n))).
Cf. A219027, A219428.
Sequence in context: A127311 A302929 A129229 * A090168 A266690 A230421
Adjacent sequences: A219026 A219027 A219028 * A219030 A219031 A219032


KEYWORD

sign


AUTHOR

V. Raman, Nov 10 2012


STATUS

approved



