OFFSET
1,5
COMMENTS
The denominators are in A241195. The new minima of phi(p-1)/(p-1) occur at primes listed in A241196. The numerator and denominator of those terms are in A241197 and A241198.
For primes p>2, the fraction phi(p - 1)/(p - 1) has the maximum value = 1/2 if and only if p is in A019434. - Geoffrey Critzer, Dec 30 2014
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 117.
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
From Amiram Eldar, Jul 31 2020: (Start)
MAPLE
seq(numer(numtheory:-phi(ithprime(i)-1)/(ithprime(i)-1)), i=1..100); # Robert Israel, Jan 11 2015
MATHEMATICA
Numerator[Table[EulerPhi[p - 1]/(p - 1), {p, Prime[Range[100]]}]]
PROG
(PARI) lista(nn) = forprime(p=2, nn, print1(numerator(eulerphi(p-1)/(p-1)), ", ")); \\ Michel Marcus, Jan 03 2015
(Magma) [Numerator(EulerPhi(NthPrime(n)-1)/(NthPrime(n)-1)): n in [1..80]]; // Vincenzo Librandi, Apr 06 2015
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
T. D. Noe, Apr 17 2014
STATUS
approved