%I #22 Jun 11 2022 05:23:54

%S 0,2,3,2,5,1,7,4,6,3,11,4,13,5,7,8,17,6,19,8,11,9,23,8,20,11,18,12,29,

%T 9,31,16,19,15,23,12,37,17,23,16,41,13,43,20,24,21,47,16,42,20,31,24,

%U 53,18,39,24,35,27,59,16,61,29,36,32,47,21,67,32

%N a(n) = phi(n) - mu(n).

%H G. C. Greubel, <a href="/A053139/b053139.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert P. Schneider, <a href="http://www.jstor.org/stable/10.4169/math.mag.87.2.132">A golden product identity for e</a>, Mathematics Magazine, Vol. 87, No. 2 (2014), pp. 132-134.

%F a(n) = n if and only if n is a prime.

%F Product_{n>=1} (1 - 1/phi^n)^(-a(n)/n) = e, where phi is the golden ratio (A001622) (Schneider, 2014). - _Amiram Eldar_, Jun 11 2022

%t a[ n_] := EulerPhi @ n - MoebiusMu @ n; Table[a[n], {n, 70}] (* _Michael Somos_, Jul 19 2011 *)

%o (PARI) {a(n) = if( n==0, 0, eulerphi( n) - moebius( n))} /* _Michael Somos_, Jul 19 2011 */

%o (Magma) [EulerPhi(n) - MoebiusMu(n): n in [1..100]]; // _G. C. Greubel_, Sep 03 2018

%Y Cf. A000010, A008683.

%Y Cf. A001113, A001622.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 25 2000