login
A008330
phi(p-1), as p runs through the primes.
43
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
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
KEYWORD
nonn,look
AUTHOR
_N. J. A. Sloane_
STATUS
approved