A281856 One fourth of the order of the abelian non-cyclic groups (Z/A033949(n)*Z)^x.

1, 1, 2, 2, 2, 3, 2, 3, 2, 4, 5, 6, 3, 6, 4, 3, 5, 6, 4, 8, 6, 10, 6, 9, 4, 9, 8, 12, 5, 8, 11, 6, 6, 10, 9, 15, 6, 8, 6, 16, 14, 10, 6, 18, 11, 15, 18, 8, 15, 10, 8, 12, 12, 9, 10, 18, 12, 9, 22, 14, 18, 24, 8, 20, 15, 9, 16, 21, 12, 10, 27, 18, 16, 11, 12, 23

Offset: 1

Author

Wolfdieter Lang, Feb 02 2017

Keywords

• nonn

Comments

a(n) is one fourth of the row product of the irregular triangle A281854.

Crossrefs

Cf. A000010, A033949, A060679, A281854.

Programs

Mathematica

EulerPhi@ Select[Range[2, 130], ! IntegerQ@ PrimitiveRoot@ # &]/4 (* Michael De Vlieger, Feb 02 2017 *)

Python

from sympy import primepi, integer_nthroot, totient
def A281856(n):
    def f(x): return int(n+1+(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 totient(m)>>2 # Chai Wah Wu, Feb 25 2025

Formula

a(n) = A000010(A033949(n))/4, n >= 1.