# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a053139 Showing 1-1 of 1 %I A053139 #22 Jun 11 2022 05:23:54 %S A053139 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 A053139 9,31,16,19,15,23,12,37,17,23,16,41,13,43,20,24,21,47,16,42,20,31,24, %U A053139 53,18,39,24,35,27,59,16,61,29,36,32,47,21,67,32 %N A053139 a(n) = phi(n) - mu(n). %H A053139 G. C. Greubel, Table of n, a(n) for n = 1..10000 %H A053139 Robert P. Schneider, A golden product identity for e, Mathematics Magazine, Vol. 87, No. 2 (2014), pp. 132-134. %F A053139 a(n) = n if and only if n is a prime. %F A053139 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 A053139 a[ n_] := EulerPhi @ n - MoebiusMu @ n; Table[a[n], {n, 70}] (* _Michael Somos_, Jul 19 2011 *) %o A053139 (PARI) {a(n) = if( n==0, 0, eulerphi( n) - moebius( n))} /* _Michael Somos_, Jul 19 2011 */ %o A053139 (Magma) [EulerPhi(n) - MoebiusMu(n): n in [1..100]]; // _G. C. Greubel_, Sep 03 2018 %Y A053139 Cf. A000010, A008683. %Y A053139 Cf. A001113, A001622. %K A053139 nonn %O A053139 1,2 %A A053139 _N. J. A. Sloane_, Mar 25 2000 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE