A070306 a(n) = 2*phi(n)/2^omega(n).

2, 1, 2, 2, 4, 1, 6, 4, 6, 2, 10, 2, 12, 3, 4, 8, 16, 3, 18, 4, 6, 5, 22, 4, 20, 6, 18, 6, 28, 2, 30, 16, 10, 8, 12, 6, 36, 9, 12, 8, 40, 3, 42, 10, 12, 11, 46, 8, 42, 10, 16, 12, 52, 9, 20, 12, 18, 14, 58, 4, 60, 15, 18, 32, 24, 5, 66, 16, 22, 6, 70, 12, 72, 18, 20, 18, 30, 6, 78, 16

Offset: 1

Author

Benoit Cloitre, May 12 2002

Keywords

• easy
• nonn

Comments

Always an integer.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Steven Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.

Crossrefs

Cf. A000010, A001221, A271547.

Programs

Mathematica

a[n_] := EulerPhi[n]/2^(PrimeNu[n] - 1); Array[a, 100] (* Amiram Eldar, Apr 29 2022 *)

PARI

for(n=1,100,print1(2*eulerphi(n)/2^omega(n),","))

Python

from sympy import totient as phi, primenu as omega
def a(n): return 2*phi(n)//2**omega(n)
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Apr 29 2022

Formula

Sum_{k=1..n} ~ c * n / sqrt(log(n)), where c = A271547/sqrt(Pi) (Finch and Sebah, 2006). - Amiram Eldar, Apr 29 2022

Extensions

Offset changed to 1 and a(1) inserted by Amiram Eldar, Apr 29 2022