OFFSET
1,2
COMMENTS
The average of the primitive roots of a prime p are <,=, or > p/2 (observation).
The indices of all primes p==1(mod 4) are in this sequence since for primes of form 4k+1 b a primitive root implies -b a primitive root.
The indices of some primes p==3 (mod 4) are also in this sequence although for most such primes the average of the primitive roots is <> p/2.(observation)
LINKS
Dimitri Papadopoulos, Table of n, a(n) for n = 1..505
EXAMPLE
p(a(1))=p(1)=2. 2 has the primitive root 1. The average primitive root is 1 and 1=2/2.
p(a(2))=p(3)=5. The primitive roots of 5 are 2 and 3. Their average equals (2+3)/phi(4)=5/2=p/2.
MATHEMATICA
A = Table[Total[Flatten[Position[Table[MultiplicativeOrder[i, Prime[k]], {i, Prime[k] - 1}], Prime[k] - 1]]]/(EulerPhi[Prime[k] - 1] Prime[k]/2), {k, 1, 1000}]; Flatten[Position[A, _?(# == 1 &)]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Dimitri Papadopoulos, Jan 08 2016
STATUS
approved