The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A048855 Number of integers up to n! relatively prime to n!. 19
 1, 1, 1, 2, 8, 32, 192, 1152, 9216, 82944, 829440, 8294400, 99532800, 1194393600, 16721510400, 250822656000, 4013162496000, 64210599936000, 1155790798848000, 20804234379264000, 416084687585280000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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 REFERENCES Ronald L. Graham, D. E. Knuth and Oren Patashnik, "Concrete Mathematics, A Foundation for Computer Science," Addison-Wesley Publ. Co., Reading, MA, 1989, page 134. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 0..450 FORMULA a(n) = phi(n!) = A000010(n!). If n is composite, then a(n) = a(n-1)*n. If n is prime, then a(n) = a(n-1)*(n-1). - Leroy Quet, May 24 2007 Under the Riemann Hypothesis, a(n) = n! / (e^gamma * log n) * (1 + O(log n/sqrt(n))). - Charles R Greathouse IV, May 12 2011 MAPLE with(numtheory):a:=n->phi(n!): seq(a(n), n=0..20); # Zerinvary Lajos, Oct 07 2007 MATHEMATICA Table[ EulerPhi[ n! ], {n, 0, 21}] (* Robert G. Wilson v, Nov 21 2003 *) PROG (Sage) [euler_phi(factorial(n)) for n in range(0, 21)] # Zerinvary Lajos, Jun 06 2009 (PARI) a(n)=eulerphi(n!) \\ Charles R Greathouse IV, May 12 2011 (Python) from math import factorial, prod from sympy import primerange from fractions import Fraction def A048855(n): return (factorial(n)*prod(Fraction(p-1, p) for p in primerange(n+1))).numerator # Chai Wah Wu, Jul 06 2022 CROSSREFS Cf. A000142, A014197. Sequence in context: A081358 A294506 A206303 * A262480 A062797 A134751 Adjacent sequences:  A048852 A048853 A048854 * A048856 A048857 A048858 KEYWORD easy,nonn AUTHOR EXTENSIONS Name changed by Daniel Forgues, Aug 01 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 26 02:05 EDT 2022. Contains 356986 sequences. (Running on oeis4.)