A219028 Number of non-primitive roots for prime(n), less than prime(n).

0, 1, 2, 4, 6, 8, 8, 12, 12, 16, 22, 24, 24, 30, 24, 28, 30, 44, 46, 46, 48, 54, 42, 48, 64, 60, 70, 54, 72, 64, 90, 82, 72, 94, 76, 110, 108, 108, 84, 88, 90, 132, 118, 128, 112, 138, 162, 150, 114, 156, 120, 142, 176, 150, 128, 132, 136, 198, 188, 184, 190

Offset: 1

Author

V. Raman, Nov 10 2012

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008330 (number of primitive roots for the n-th prime, less than n-th prime).

Cf. A046144 (number of primitive roots for n, less than n).

Cf. A010554 (value of phi(phi(n))).

Programs

Mathematica

Table[c=Prime[n];c-1-EulerPhi[EulerPhi[c]],{n,70}] (* Harvey P. Dale, Feb 12 2013 *)

PARI

forprime(i=2,600,p=0;for(q=1,i-1,if(znorder(Mod(q,i))!=eulerphi(i),p++));print1(p","))

Formula

a(n) = p - 1 - phi(phi(p)), where p is the n-th prime.

a(n) = p - 1 - A008330(n) = p - 1 - A010554(p), where p is the n-th prime. - V. Raman, Nov 22 2012