%I #8 Jun 28 2013 05:06:37

%S 0,0,2,3,4,4,6,5,6,7,9,5,10,7,10,11,12,6,14,7,14,15,16,5,18,13,17,13,

%T 20,7,24,9,18,19,22,15,28,10,22,19,28,9,32,9,26,27,30,5,34,17,33,25,

%U 32,7,38,23,36,29,34,5,46

%N The number of positive integers <= n that are not strongly prime to n.

%C k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.

%C a(n) = n - phi(n) + tau(n-1) if n > 0 and a(0) = 0.

%C Here phi(n) = A000010(n) and tau(n) = A000005(n).

%H Peter Luschny, <a href="http://www.oeis.org/wiki/User:Peter_Luschny/StrongCoprimality">Strong coprimality</a>.

%e a(11) = 11 - card({3,4,6,7,8,9}) = 5.

%p with(numtheory):

%p A181833 := n -> `if`(n=0,0,n-phi(n)+tau(n-1));

%p A181833a := n -> n - A181830(n);

%t a[n_] := Select[Range[n], Not[CoprimeQ[#, n] && !Divisible[n-1, #]] &] // Length; a[1] = 0; Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Jun 28 2013 *)

%Y Cf. A181830, A181831, A181832, A181834, A181835, A181836, A051953.

%K nonn

%O 0,3

%A _Peter Luschny_, Nov 17 2010