A175594 Numbers having no primitive root.

0, 8, 12, 15, 16, 20, 21, 24, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 51, 52, 55, 56, 57, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 84, 85, 87, 88, 90, 91, 92, 93, 95, 96, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114, 115, 116, 117, 119, 120, 123

Offset: 1

Author

Vladislav-Stepan Malakhovsky and Juri-Stepan Gerasimov, Jul 20 2010

Keywords

• nonn

Comments

Union of {0} and A033949.

Numbers n such that A046145(n)=0 except n=1.

Programs

Mathematica

Prepend[Select[Range[2, 123], Not[IntegerQ[PrimitiveRoot[#]]] &], 0] (* Alonso del Arte, Dec 12 2011 *)

Python

from sympy import primepi, integer_nthroot
def A175594(n):
    if n==1: return 0
    def f(x): return int(n+(x>=2)+(x>=4)+sum(primepi(integer_nthroot(x,k)[0])-1 for k in range(1,x.bit_length()))+sum(primepi(integer_nthroot(x>>1,k)[0])-1 for k in range(1,x.bit_length()-1)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 25 2025

Extensions

Corrected by R. J. Mathar, Oct 15 2011

Corrected by Arkadiusz Wesolowski, Sep 06 2012