A008330 phi(p-1), as p runs through the primes.

1, 1, 2, 2, 4, 4, 8, 6, 10, 12, 8, 12, 16, 12, 22, 24, 28, 16, 20, 24, 24, 24, 40, 40, 32, 40, 32, 52, 36, 48, 36, 48, 64, 44, 72, 40, 48, 54, 82, 84, 88, 48, 72, 64, 84, 60, 48, 72, 112, 72, 112, 96, 64, 100, 128, 130, 132, 72, 88, 96, 92, 144, 96, 120, 96, 156, 80, 96, 172, 112

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

Maple

A008330 := proc(n)
    numtheory[phi](ithprime(n)-1) ;
end proc:
seq(A008330(n), n=1..100) ;

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

Cf. A000010, A241194, A241195 (fraction phi(p-1)/(p-1)), A338364 (partial products).

Sequence in context: A336125 A353125 A330807 * A191234 A225373 A138219

Adjacent sequences: A008327 A008328 A008329 * A008331 A008332 A008333

Keyword

nonn,look

Author

N. J. A. Sloane

Status

approved