%I
%S 1,1,1,2,8,32,192,1152,9216,82944,829440,8294400,99532800,1194393600,
%T 16721510400,250822656000,4013162496000,64210599936000,
%U 1155790798848000,20804234379264000,416084687585280000
%N Number of integers up to n! relatively prime to n!.
%C Rephrasing the Quet formula: Begin with 1. Then, if n + 1 is prime subtract 1 and multiply. If n+1 is not prime, multiply. Continue writing each product. Thus the sequence would begin 1, 2, 8, . . . . The first product is 1*(2  1), second is 1*(3  1), and third is 2*4.  _Enoch Haga_, May 06 2009
%D Ronald L. Graham, D. E. Knuth and Oren Patashnik, "Concrete Mathematics, A Foundation for Computer Science," AddisonWesley Publ. Co., Reading, MA, 1989, page 134.
%H Charles R Greathouse IV, <a href="/A048855/b048855.txt">Table of n, a(n) for n = 0..450</a>
%F a(n) = phi(n!) = A000010(n!).
%F If n is composite, then a(n) = a(n1)*n. If n is prime, then a(n) = a(n1)*(n1).  _Leroy Quet_, May 24 2007
%F Under the Riemann Hypothesis, a(n) = n! / (e^gamma * log n) * (1 + O(log n/sqrt(n))).  _Charles R Greathouse IV_, May 12 2011
%p with(numtheory):a:=n>phi(n!): seq(a(n), n=0..20); # _Zerinvary Lajos_, Oct 07 2007
%t Table[ EulerPhi[ n! ], {n, 0, 21}] (* _Robert G. Wilson v_, Nov 21 2003 *)
%o (Sage) [euler_phi(factorial(n)) for n in range(0,21)] # _Zerinvary Lajos_, Jun 06 2009
%o (PARI) a(n)=eulerphi(n!) \\ _Charles R Greathouse IV_, May 12 2011
%Y Cf. A000142, A014197.
%K easy,nonn
%O 0,4
%A _Paul Max Payton_
%E Name changed by _Daniel Forgues_, Aug 01 2011
