A219027 Number of non-primitive roots for n, less than n.

0, 0, 1, 2, 2, 4, 4, 7, 6, 7, 6, 11, 8, 11, 14, 15, 8, 15, 12, 19, 20, 17, 12, 23, 16, 21, 20, 27, 16, 29, 22, 31, 32, 25, 34, 35, 24, 31, 38, 39, 24, 41, 30, 43, 44, 35, 24, 47, 36, 41, 50, 51, 28, 47, 54, 55, 56, 45, 30, 59, 44, 53, 62, 63, 64, 65, 46, 67, 68

Offset: 1

Author

V. Raman, Nov 10 2012

Keywords

• nonn

Comments

a(n) will be the same as A219029(n) except when n is a member of A033949 or n = 1, i.e. n is not 2, 4, prime, power of a prime, twice a prime, or twice a prime power. In such cases, when n is a member of A033949, then a(n) = n-1.

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))).

Cf. A219029.

Programs

PARI

for(i=1,100,p=0;for(q=1,i-1,if(gcd(q,i)>1||znorder(Mod(q,i))!=eulerphi(i),p++));print1(p","))

Formula

n-1-A046144(n).