OFFSET
2,3
COMMENTS
The resilience of a denominator, R(d), is the ratio of proper fractions n/d, 0 < n < d, that are resilient, i.e., such that gcd(n,d)=1. Obviously this is the case for phi(d) proper fractions among the d-1 possible ones.
a(n) = 1 if and only if n is prime. - Robert Israel, Dec 26 2016
LINKS
Robert Israel, Table of n, a(n) for n = 2..10000
Project Euler, Problem 245: resilient fractions, May 2009
EXAMPLE
a(9)=4 since for the denominator d=9, among the 8 proper fractions n/9 (n=1,...,8), six cannot be canceled down by a common factor (namely 1/9, 2/9, 4/9, 5/9, 7/9, 8/9), thus R(9) = 6/8 = 3/4.
MAPLE
seq(denom(numtheory:-phi(n)/(n-1)), n=2..100); # Robert Israel, Dec 26 2016
MATHEMATICA
Denominator[Table[EulerPhi[n]/(n-1), {n, 2, 90}]] (* Harvey P. Dale, Apr 18 2012 *)
PROG
(PARI) A160496(n)=denominator(eulerphi(n)/(n-1))
(Magma) [Denominator(EulerPhi(n)/(n-1)): n in [2..80]]; // Vincenzo Librandi, Jan 02 2017
CROSSREFS
KEYWORD
nonn,look
AUTHOR
M. F. Hasler, May 23 2009
STATUS
approved