login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048855 Number of integers up to n! relatively prime to n!. 18
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 xrange(0, 21)] # Zerinvary Lajos, Jun 06 2009

(PARI) a(n)=eulerphi(n!) \\ Charles R Greathouse IV, May 12 2011

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

Paul Max Payton

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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 17 19:35 EST 2017. Contains 294834 sequences.