OFFSET
1,3
COMMENTS
Number of primitive roots in the field with p elements.
Kátai proves that phi(p-1)/(p-1) has a continuous distribution function. - _Charles R Greathouse IV_, Jul 15 2013
For odd primes p, phi(p-1)<=(p-1)/2 since p has phi(p-1) primitive roots and (p-1)/2 quadratic residues and no primitive root is a quadratic residue. - _Geoffrey Critzer_, Apr 18 2015
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
P. Erdős, On the density of some sequences of numbers, III., J. London Math. Soc. 13 (1938), pp. 119-127.
Imre Kátai, On distribution of arithmetical functions on the set prime plus one, Compositio Math. 19 (1968), pp. 278-289.
I. J. Schoenberg, Über die asymptotische Verteilung reeller Zahlen mod 1, Mathematische Zeitschrift 28:1 (1928), pp. 171-199.
FORMULA
a(n) = phi(phi(prime(n))). - _Robert G. Wilson v_, Dec 26 2015
a(n) = phi(A006093(n)). - _Michel Marcus_, Dec 27 2015
MATHEMATICA
Table[ EulerPhi[ Prime@n - 1], {n, 70}] (* _Robert G. Wilson v_, Dec 17 2005 *)
PROG
(PARI) a(n)=eulerphi(prime(n)-1) \\ _Charles R Greathouse IV_, Dec 08 2011
(Magma) [EulerPhi(NthPrime(n)-1): n in [1..80]]; // _Vincenzo Librandi_, Apr 06 2015
CROSSREFS
KEYWORD
nonn,look
AUTHOR
_N. J. A. Sloane_
STATUS
approved