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A008330
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phi(p-1), as p runs through the primes.
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43
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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a(n) = phi(phi(prime(n))). - Robert G. Wilson v, Dec 26 2015
a(n) = phi(A006093(n)). - Michel Marcus, Dec 27 2015
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MAPLE
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A008330 := proc(n)
numtheory[phi](ithprime(n)-1) ;
end proc:
seq(A008330(n), n=1..100) ;
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MATHEMATICA
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Table[ EulerPhi[ Prime@n - 1], {n, 70}] (* Robert G. Wilson v, Dec 17 2005 *)
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PROG
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(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
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CROSSREFS
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Cf. A000010, A241194, A241195 (fraction phi(p-1)/(p-1)), A338364 (partial products).
Sequence in context: A175359 A336125 A330807 * A191234 A225373 A138219
Adjacent sequences: A008327 A008328 A008329 * A008331 A008332 A008333
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KEYWORD
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nonn,look
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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