login
a(n) = 2*phi(n)/2^omega(n).
3

%I #16 Apr 30 2022 08:20:55

%S 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,

%T 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,

%U 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

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

%C Always an integer.

%H Amiram Eldar, <a href="/A070306/b070306.txt">Table of n, a(n) for n = 1..10000</a>

%H Steven Finch and Pascal Sebah, <a href="http://arXiv.org/abs/math.NT/0604465">Squares and Cubes Modulo n</a>, arXiv:math/0604465 [math.NT], 2006-2016.

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

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

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

%o (Python)

%o from sympy import totient as phi, primenu as omega

%o def a(n): return 2*phi(n)//2**omega(n)

%o print([a(n) for n in range(1, 43)]) # _Michael S. Branicky_, Apr 29 2022

%Y Cf. A000010, A001221, A271547.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, May 12 2002

%E Offset changed to 1 and a(1) inserted by _Amiram Eldar_, Apr 29 2022